puzzle

2007-12-31T12:23:00.000-08:00

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PUZZLE LINKS

2007-07-16T05:05:00.000-07:00

LINKS
A series of online riddles

 Puzzles based on GK, Logic and Technical Knowledge.
 First one to solve them all wins.
 Cash prize will be awarded to the winner
 Puzzle kicks off on Friday 4th August at 9:00 a.m.
Will continue till 19th August.
 Register for free at Technovanza website ( www.technovanza.org )
 Based on the lines of Notpron and Klueless.
http://wpc.puzzles.com/links/index.htm
Amit there are lots of such sits.
"pqrst" is a popular puzzle site which runs competitions regularly.
its available at
http://www.otuzoyun.com/pqrst/
quarterly competation...
this one is like pqrst...

http://diogen.h1.ru/english/ipst.html
Puzzle Site
This one is one of my favourites:

http://perplexus.info/
http://www.geocities.com/hnene/puzzles/puzzles.html
http://www.brainvista.com
Word Puzzle Game....
This is one of the coolest games, (I am quiet addicted to this game! LOL)
There is a riddle and u have to solve it to save a KANGAROO,
u wil only be given 4 chances, if u r wrong, then the KANGAROO will be HANGED (HANGAROO....)
Try and tell how far u have gone (I mean the no. of levels)
Dont forget to bookmark, cuz thats the coolest game....

Here is the link, I'll try to load another link too if possible....
http://puzzl.50webs.com/hangaroo.htm
hey guys just give this test .link is
http://web.tickle.com/tests/braintwister/authorize/signin.jsp?url=/tests/braintwister/index.jsp

its a good one
Wackiest picture puzzle
This is the wackiest picture puzzle I have ever seen,
there are 12 members in the pic, and after a swap there are 13!!!
From where the 1 came????? After another swap again its 12....
Find out if u can....

http://tutor2.brinkster.net/puzzle/missing.htm

THE BEST IQ Test U CAN GET......
try this IQ test..!
its gr88

http://www.highiqsociety.org/iq_tests/
http://www.brainbashers.com/

puzzle-loop.com/" target="_blank">http://www.puzzle-loop.com/

http://www.saidwhat.co.uk/games/kakuro/standardkakuro3.php

puzzle-bridges.com/" target="_blank">http://www.puzzle-bridges.com/

puzzle-sudoku.net/" target="_blank">http://www.puzzle-sudoku.net/

http://neutralriddle.50webs.com/

Download soduku software from below link

http://www.ppclink.com/index.php?ppclink=product&do=view&id=46

Maths puzzles

http://www.mathpuzzle.com/

C quiz

http://c-faq.com/questions.html

http://www.cprogramming.com/

http://analysingc.50webs.com/

check this game out

http://www.planetdan.net/pics/misc/georgie.htm

http://www.toilette-humor.com/maze-child.html
PUZZLE
http://discuss.fogcreek.com/techInterview/default.asp
Puzzle
Puzzle...

here's the link

http://www.distortedriddle.com/

http://asptutors.brinkster.net/puzzles/couples.htm

Math puzzles
http://www.mathpuzzle.com/
http://www.maa.org/news/mathgames.html

Mar 7

Company Puzzles

2007-05-29T22:22:00.000-07:00

Three Switches


Problem Statement:

You are standing in a hallway next to three light switches, all of which are off. Each switch operates a different incandescet light-bulb in the room at the end of the hall. You cannot see the lights from where the switches are. Determine which light corresponds to each switch. You may go into the room with the lights only once.

Solution:

1) Turn on any one switches. Let them be 1st switch.

2) After some time turn off the 1st switch and turn on 2nd switch.

Now go to the room

- If the bulb glowing then right switch whhich is current on.
- If the bulb not currently glowing but itt is hot(because it was on for some time before turning it off), then the right switch is first one.
- Else right switch is third one.

2 eggs problem



Prolem Statement:

* You are given 2 eggs.
* You have access to a 100-storey building.
* Eggs can be very hard or very fragile means it may break if dropped from the first floor or may not even break if dropped from 100 th floor.Both eggs are identical.
* You need to figure out the highest floor of a 100-storey building an egg can be dropped without breaking.
* Now the question is how many drops you need to make. You are allowed to break 2 eggs in the process



If you are one of the people who likes to solve a puzzle before seeing the answer you must quit the blog now and come back later for checking the answer.


Now that this is a Google interview question I am taking the normal "Interview-Style" of solving a problem. Simply saying thinking aloud through the solution from worst to the best correcting the flows optimizing the solution or taking the 5-minute hard thinking acting pause to a problem, which you know already and just want to make your interviewer think that you are a challenge lover.


Solution

Drop the first egg from 50.If it breaks you can try the same approach for a 50-storey building (1 to 49) and try it from 25th floor. If it did not break try at 75th floor. And use linear search with the remaining portion of storey we need to test. For example if the first egg breaks at 50 we need to try all possibilities from 1 to 49.

Now this looks a feasible solution. In computer student's jargon do a binary search with first egg and linear search with the second one. Best case is log (100) and worst is 50.


Now the optimal solution for the problem is that you figure out that you will eventually end up with a linear search because you have no way of deciding the highest floor with only one egg (If you broke one egg and you have to find the answer among 10 all you can do is start from the lowest to the highest and the worst is the total number of floors). So the whole question grinds up to how to make use of the first egg to reduce the linear testing of the egg.


(For strict computer science students, well this problem can be solved using binary search on the number of drops needed to find the highest floor.)

Now let x be the answer we want, the number of drops required.

So if the first egg breaks maximum we can have x-1 drops and so we must always put the first egg from height x. So we have determined that for a given x we must drop the first ball from x height. And now if the first drop of the first egg doesn’t breaks we can have x-2 drops for the second egg if the first egg breaks in the second drop.

Taking an example, lets say 16 is my answer. That I need 16 drops to find out the answer. Lets see whether we can find out the height in 16 drops. First we drop from height 16,and if it breaks we try all floors from 1 to 15.If the egg don’t break then we have left 15 drops, so we will drop it from 16+15+1 =32nd floor. The reason being if it breaks at 32nd floor we can try all the floors from 17 to 31 in 14 drops (total of 16 drops). Now if it did not break then we have left 13 drops. and we can figure out whether we can find out whether we can figure out the floor in 16 drops.

Lets take the case with 16 as the answer

1 + 15 16 if breaks at 16 checks from 1 to 15 in 15 drops
1 + 14 31 if breaks at 31 checks from 17 to 30 in 14 drops
1 + 13 45 .....
1 + 12 58
1 + 11 70
1 + 10 81
1 + 9 91
1 + 8 100 We can easily do in the end as we have enough drops to accomplish the task


Now finding out the optimal one we can see that we could have done it in either 15 or 14 drops only but how can we find the optimal one. From the above table we can see that the optimal one will be needing 0 linear trials in the last step.

So we could write it as

(1+p) + (1+(p-1))+ (1+(p-2)) + .........+ (1+0) >= 100.

Let 1+p=q which is the answer we are looking for

q (q+1)/2 >=100

Solving for 100 you get q=14.
So the answer is: 14
Drop first orb from floors 14, 27, 39, 50, 60, 69, 77, 84, 90, 95, 99, 100... (i.e. move up 14 then 13, then 12 floors, etc) until it breaks (or doesn't at 100).

Coins on the table


Problem Statement:

There is a table on which a number of coins are placed. You also know that there are as many coins with Head up as many coins with Tail up. Now you have to divide the coins (number of coins is even) into two equal piles such that number of coins with Heads up and Tails up in either piles be the same. The catch is you are blind folded and you cannot determine the sides (for sure) if you are blinded.

Solution:

Divide the coins in half by quantity (easy to count coins while blindfolded)

Then, flip all the coins in one pile over.

Bridge Crossing

 Problem Statement:

A party of four travelers come to a ricety bridge at night. The bridge can hold the weight of at most two of the travelers at a time, and it cannot be crossed without using a flashlight. The tavelers have one flashlight among them. Each traveler walks at a different speed: The first can cross the bridge in 1 minute, the second in 2 minutes, the third in 5 minutes, and the fourth taes 10 minutes to cross the bridge . If two travelers cross together, they walk at the speed of slower traveler.

What is the least amount of time in which all the travelers can cross from one side of the bridge to the other.

Solution:

To minimize the total time, we need to send those traveler together who takes more time.

- first(1) and second(2) traveler go acrooss     (2 minutes)
- first traveler(1) goes back             (3 minuttes)
- thord(5) and fourth(10) traveler cross      (13 minutes)
- Second Traveler (2) goes back         (15 minnutes)
- First(1)  and second(2) traveler cross      (17 minutes)

Ans: 17 minutes

Camel and Bananas


Prblem Statement:

A camel must travel 1000 miles across a desert to the nearest city. She has 3000 bananas but can only carry 1000 at a time. For every mile she walks, she needs to eat a banana. What is the maximum number of bananas she can transport to the city?


Solution Description:

Let's begin by imagining how the camel might get the bananas across the desert. If she starts off with 1000 bananas and carries them 1000 miles, she won't be able to return for the rest of them because she won't have any bananas to fuel her trip back. She won't have any bananas to give to her friends either, because she will have eaten them all during the journey. This suggests that the camel needs to cache piles of bananas at certain points in the desert so she can actually move some of them instead of using them all for fuel.

Suppose the camel does this:

 1. Pick up 1000 bananas.
 2. Carry them one mile into the desert, eating one on the way.
 3. Keep one of the bananas for the trip back.
 4. Repeat steps (1-3).
 5. Repeat steps (1-2).

At the end of this, there will be 2995 bananas, which are 999 miles from the city. The camel will also be 999 miles from the city.

So in effect, she now has a smaller version of the same problem. Of course, it cost her 5 bananas to move the rest a mile. If she keeps this up, she won't have any bananas left when she gets to the city.

However, at this point, she can pick up 1000 bananas, eat 999 on the way to the city, and have 1 left over when she gets there. It's not nothing, but it's hard not to think that she could do better. And she still won't be able to go back for the 1995 bananas that she left behind.

Can we generalize the strategy? Suppose she does this:

 1. Pick up 1000 bananas.
 2. Carry them N miles into the desert, eating N on the way.
 3. Keep N of the bananas for the trip back.
 4. Repeat steps (1-3).
 5. Repeat steps (1-2).

Again, she ends up with a smaller version of the problem. Now she has (3000-5N) bananas, and is (1000-N) miles from the city.

At this point, we might ask a few questions:

 1. If she simply repeats this strategy, what value of N would allow her to get the most uneaten bananas to the city?

 2. Would she have to repeat the strategy exactly? For example, at some point, she might get down to 2000 bananas. Then it would only cost her 3N bananas (rather than 5N) to move the rest N miles.

 3. Should she always pick up 1000 bananas when she wants to move some of them farther into the desert? Could there be an advantage to making more trips with smaller loads? Could there be an advantage to leaving some of the bananas at the starting point, and ignoring them completely?

Solution:

Camel will need 5 bananas to transfer all the bananas 1 mile away...
5 as for 1st 1000 he'll go n come back then for another 1000 he'll go n come back but for last 1000 he'll only go as nothing will be left behind...

For second mile too it'll take 5 bananas...

Now it'll require 5 bananas per mile for total banana count > 2000
and for banana count < 2000 it'll eat 3 bananas...

and for < 1000 it'll eat 1 banana....

so 1st 1000 bananas will be finished in 1000/5 = 200 Miles
next 1000 in 1000/3 = 334 Miles...

Finaly he'll have 1000 bananas and 466 miles to go...

At B camel will have 534 bananas

25 Horses Race


Problem Statement:

There are 25 horses and in what min no of races can u find top three of them
The constraints are that in one race u can race 5 of the horses and u dont have a timer...

Solution:

divide 25 horses in 5 groups for 5 races
Now take toppers of all the races for another race....  6th Race

Now in this race the 4th and 5th are out because we want only top 3....

2nd and 3rd of the group of third horse in 6th race are also out...as they will have position lower than 3 in 25 horses togethar...

3rd horse of the group of second horse in 6th race is also out for same reason
take tooper of 6th race out as this will be topper of all 25 horses

Now we have 5 horses and we want top 2 of them.... 1 more race

Ans: 7 races

50 black and 50 white ball probability problem


Problem Statement:

There are two empty urns in a room. You have 50 white balls and 50 black balls. After you place the balls in the urns, a random ball will be picked from a random urn. Distribute the balls (all of them) into the urns to maximize the chance of picking a white ball.

Solution:

Place one white in one urn, and all the others in the other urn. This gives a 74/99 probability of picking white.

explanation:

probability of picking white ball from which only one white ball is there = 1
probability of picking white ball from which 49 white and 50 black ball is there = 49/99

probability of picking white ball = (1 + 49/99)/2

13 balls problem


Problem Statement:

The general problem is you will be given n balls and one of them is either heavier or lighter and you are asked to find out the minimum number of weighings using a common balance required to find out the odd one out.

Example 1: 8 Balls,Odd ball being heavier

This is the simplest question among the lot and is often used during phone screenings.The question is to find out the minimum number of weighings required to spot the odd heavier ball among 8 identically looking balls using a common balance.Answer is 2 and the solution is given in the next paragraph.

For simplicity let us name the balls as A1,A2,A3,B1,B2,B3,C1 and C2.We weigh with A's on one side and B's on the other side of the balance.If both sides are equal this means the heavier odd ball is among C1 and C2.We can figure out the heavier ball with one more weighing.If A's are heavier than B's then the heavier odd ball is among A's.Now we balance A1 and A2.If both are same then A3 is the odd ball or else the heavier one of A1 and A2 .Thus, we can find out the heavier ball using only 2 weighings.



Example 2: 8 Balls,Odd ball can be either heavier or lighter than the rest.

This is a little trickier to solve.Let us name the 8 balls as A1,A2,A3,B1,B2,B3,C1 and C2.Now weigh with A1,A2,A3 on one side and B1,B2,B3 on the other side.If both weigh equal then the odd ball is among C1 and C2.Now we know that A's and B's are all normal ones we can weigh C1 with A1 and check whether C1 weighs the same as the normal ball.In this way, we can figure out in one weigh which of C1 and C2 is odd.Now if A's weighed more than B's then we know for sure C's are normal ones.Now lets assume A's heavier than B's and we still don't know whether the odd is among A's or B's.

We know
A1 A2 A3 <>

puzzle discussion

2007-05-29T22:21:00.000-07:00

Coins on the table	6	itsme	240	Mon May 28, 2007 5:32 pm sam
	sutable seat	2	rahul	144	Fri May 11, 2007 5:18 pm Guest
	nterview puzzles used at Google	7	guest	299	Fri Apr 13, 2007 6:55 am rekha
	for u guddu	1	sairam	101	Wed Apr 11, 2007 7:47 am guddu
	whats that	1	sairam	66	Wed Apr 11, 2007 7:45 am Guest
	10 gud puzzel	1	guddu	141	Tue Apr 10, 2007 8:56 am guest
	water gallon	1	guddu	68	Tue Apr 10, 2007 8:55 am guest
	choose socks	1	guddu	56	Tue Apr 10, 2007 8:53 am guest
	what is the initial amount held with the merchant	2	sairam	61	Tue Apr 10, 2007 6:40 am guddu
	Camel and Bananas	3	itsme	187	Tue Mar 27, 2007 12:35 pm rakesh
	WEDDING	3	Ajit	118	Tue Mar 27, 2007 8:05 am Aksah
	13 balls problem	1	itsme	169	Tue Mar 27, 2007 6:35 am pramod_jnumca@yahoo.com
	25 Horses Race	2	itsme	239	Tue Mar 27, 2007 6:31 am pramod_jnumca@yahoo.com
	2 egg puzzle

Practice Puzzle 4 Answers

2007-05-29T22:20:00.001-07:00

1) Start with ZBG and ZBGJ. It should be either "the/then" or "you/your" combination as they appear more.

B R W Q H L F K W H J K Q I B W K
o b s t a c l e s a r e t h o s e

Q I C E D W Z B G W K K M I K E
t h i n g s y o u s e e w h e n

Z B G Q H S K Z B G J K Z K W
y o u t a k e y o u r e y e s

B U U Z B G J D B H F W.
o f f y o u r g o a l s.

2) It is obvious that between 5 O'clock and 6 O'clock the hands will not be exactly opposite to each other. It is also obvious that the hands will be opposite to each other just before 5 O'clock. Now to find exact time:

The hour hand moves 1 degree for every 12 degrees that the minute hand moves. Let the hour hand be X degree away from 5 O'clock. Therefore the minute hand is 12X degree away from 12 O'clock.

Therefore solving for X

Angle between minute hand and 12 O'clock + Angle between 12 O'clock and 4 O'clock + Angle between 4 O'clock and hour hand = 180
12X + 120 + (30-X) = 180
11X = 30
Hence X = 30/11 degrees
(hour hand is X degree away from 5 O'clock)

Now each degree the hour hand moves is 2 minutes.

Therefore minutes are
= 2 * 30/11
= 60/11
= 5.45 (means 5 minutes 27.16 seconds)

Therefore the exact time at which the hands are opposite to each other is
= 4 hrs. 54 min. 32.74 seconds

3) They took their percentages from 40 and not from 39, so they got more than their share.

The oldest son got 1/2 of 40 = 20 which is 0.5 more
The second son got 1/4 of 40 = 10 which is 0.25 more
The third son got 1/8 of 40 = 5 which is 0.125 more
The youngest son got 1/10 of 40 = 4 which is 0.1 more

And the stranger got 1/40 of 40 = 1 which is 0.025 more (As he is not supposed to get anything)

All these fractions add to = 0.5 + 0.25 + 0.125 + 0.1 + 0.025 = 1 which stranger took away.

4) There are total 2 couples and a son. Grandfather and Grand mother, their son and his wife and again their son. So total 5 people.

Grandfather, Grandmother
|
|
Son, wife
|
|
Son

5) He lost Rs.600

First time restaurant has given food worth Rs.105 and Rs. 395 change. Similarly second time, food worth Rs.80 and Rs.20 change. Here, we are not considering food restaurant profits.

6) 3651 represents LENS.

Let's assign possible values to each letter and then use trial-n-error.

S must be 1.

Then D (under L) must be greater than 5. If D is 6, then L is 0. But then A must be 0 or 1 which is impossible. Hence, the possible values of D are 7, 8 or 9.

N must be E + 1. Also, D must be A + 5 as the possible values of D are 7, 8 or 9, D can not be (10+A) + 5.

Now using trial-n-error, we get S=1, I=2, L=3, A=4, N=5, E=6 and D=9

S L I D E 1 3 2 9 6

- D E A N - 9 6 4 5

----- -----

3 6 5 1 L E N S

Hence, 3651 represents LENS.

7) Clark is the landlord.

Assume each statement true, one at a time and see that no other statement is contradicted.

Let's assume that Statement (1) is true. Then, Adam is the landlord and lives in apartment 1. Also, other three's apartments will be on the right of his apartment - which contradicts Statement (4) i.e. If Edmund's apartment is right of Adam's apartment, then the landlord is Burzin. Thus, Adam is not the landlord.

Let's assume that Statement (2) is true. Then, Edmund is the landlord and lives in apartment 4. Also, other three's apartments will be on the left of his apartment - which again contradicts Statement (4) i.e. If Edmund's apartment is right of Adam's apartment, then the landlord is Burzin. Thus, Edmund is not the landlord either.

Let's assume that Statement (3) is true. Then, Clark is the landlord and lives in apartment 3. It satisfies all the statements for
(1) Adam - (2) Edmund - (3) Clark - (4) Burzin

Hence, Clark is the landlord.

Similarly, you can assume Statement (4) true and find out that it also contradicts.

8) J is the married man.

Note that a person's sister-in-law may be the wife of that person's brother or the sister of that person's spouse.

There are 2 cases:

If B's legal spouse is J, then J's sibling must be P and P's sister-in-law must be B.

If B's legal spouse is P, then P's sister-in-law must be J and J's sibling must be B.

It is given that B's legal spouse and J's sibling are of the same sex. Also, it is obvious that P's sister-in-law is female. Then, B's legal spouse and J's sibling both must be males.

B's spouse J's sibling P's sister-in-law

(male) (male) (female)

Case I J P B

Case II P B J

Case II is not possible as B & P are married to each other and both are male. Hence, J is the married man.

9) 44

36 of the cubes have EXACTLY 2 of their sides painted black, but because a cube with 3 of its sides painted black has 2 of its sides painted black, you must also include the corner cubes. This was a trick question, but hopefully the title of the puzzle tipped you off to this.

10) t takes 5 moves to make the triangle with 5 rows point the other way.

0 = a coin that has not been moved.
X = the old position of the moved coin
8 = the new position of the moved coin.

________X
_______X X
____8 0 0 0 8
_____0 0 0 0
____X 0 0 0 X
_______8 8
________8

For traingle of any number of rows, the optimal number of moves can be achieved by moving the vertically symmetrical coins i.e. by moving same number of coins from bottom left and right, and remaining coins from the top.

For a triangle with an odd number of rows, the total moves require are :
(N^2/4) - (N-4) Where N = 4, 6, 8, 10, ...

For a triangle with even number of rows, the total moves require are :
((N^2-1)/4) - (N-4) Where N = 5, 7, 9, 11, ...

11) Each envelope contains the money equal to the 2 raised to the envelope number minus 1. The sentence "Each envelope contains the least number of bills possible of any available US currency" is only to misguide you. This is always possible for any amount !!!

One more thing to notice here is that the man must have placed money in envelopes in such a way that if he bids for any amount less than $25000, he should be able to pick them in terms of envelopes.

First envelope contains, 2^0 = $1
Second envelope contains, 2^1 = $2
Third envelope contains, 2^2 = $4
Fourth envelope contains, 2^3 = $8 and so on...

Hence the amount in envelopes are $1, $2, $4, $8, $16, $32, $64, $128, $256, $512, $1024, $2048, $4096, $8192, $8617

Last envelope (No. 15) contains only $8617 as total amount is only $25000.

Now as he bids for $8322 and gives envelope number 2, 8 and 14 which contains $2, $128 and $8192 respectively.

Envelope No 2 conrains one $2 bill
Envelope No 8 conrains one $100 bill, one $20 bill, one $5 bill, one $2 bill and one $1 bill
Envelope No 14 conrains eighty-one $100 bill, one $50 bill, four $10 bill and one $2 bill

12) The minute and the hour hand meet 11 times in 12 hours in normal watch i.e. they meet after every
= (12 * 60) / 11 minutes
= 65.45 minutes
= 65 minutes 27.16 seconds

But in our case they meet after every 65 minutes means the watch is gaining 27.16 seconds.

13) The number is 45, simply because
45 = 5 * (4 + 5)
How does one find this number?

Let T be the digit in the tens place and U be the digit in the units place. Then, the number is 10*T + U, and the sum of its digits is T + U.

The following equation can be readily written:
10*T + U = 5*(T + U) or
10*T + U = 5*T + 5*U or
5*T = 4*U

Thus, T / U = 4 / 5

Since T and U are digits, T must be 4 and U must be 5.

14) Total no of balls = 5 + 7 + 14 + 16 + 18 + 29 = 89

Total number of balls are odd. Also, same number of red balls and blue balls are left out after selling one box. So it is obvious that the box with odd number of balls in it is sold out i.e. 5, 7 or 29.

Now using trial and error method,
(89-29) /2 = 60/2 = 30 and
14 + 16 = 5 + 7 + 18 = 30

So box with 29 balls is sold out.

15) 47 Chocolates and 16 Friends

Let's assume that there are total C chocolates and F friends.

According to first case, if she gives 3 chocolates to each friend, one friend will get only 2 chocolates.
3*(F - 1) + 2 = C

Similarly, if she gives 2 chocolates to each friends, she will left with 15 chocolates.
2*F + 15 = C

Solving above 2 equations, F = 16 and C = 47. Hence, Ekta got 47 chocolates and 16 friends

16) Esha's age is 45 years.

Assume that Esha's age is 10X+Y years. Hence, her hunsbands age is (10Y + X) years.

It is given that difference between their age is 1/11th of the sum of their age. Hence,
[(10Y + X) - (10X + Y)] = (1/11)[(10Y + X) + (10X + Y)]
(9Y - 9X) = (1/11)(11X + 11Y)
9Y - 9X = X + Y
8Y = 10X
4Y = 5X

Hence, the possible values are X=4, Y=5 and Esha's age is 45 years.

17) The fish is 128 inches long.

It is obvious that the lenght of the fish is the summation of lenghts of the head, the body and the tail. Hence,
Fish (F) = Head (H) + Body (B) + Tail (T)

But it is given that the lenght of the head is 4 inches i.e. H = 4. The body is three-quarters of its total length i.e. B = (3/4)*F. And the tail is its head plus a quarter the lenght of its body i.e. T = H + B/4. Thus, the equation is
F = H + B + T
F = 4 + (3/4)*F + H + B/4
F = 4 + (3/4)*F + 4 + (1/4)*(3/4)*F
F = 8 + (15/16)*F
(1/16)*F = 8
F = 128 inches

Thus, the fish is 128 inches long.

18) Everybody in the World will get to know the scandal in 8 hours.

You came to know of a scandal and you passed it on to 4 persons in 30 minutes. So total (1+4) 5 persons would know about it in 30 minutes.

By the end of one hour, 16 more persons would know about it. So total of (1+4+16) 21 persons would know about it in one hour.

Similarly, the other (1+4+16+64) persons would have know about it in one and a half hours. (1+4+16+64+256) persons would have know about it in two hours and so on...

It can be deduced that the terms of the above series are the power of 4 i.e. 4^0, 4^1, 4^2, 4^3 and so on upto (2N+1) terms. Also, the last term would be 4^2N where N is the number of hours.

Sum of the above mentioned series = [4^(2N+1)-1]/3

***END OF ANSWER SESSION FOR PRACTISE PUZZLES _3 ******

Thanks,
All The Best

Practice Puzzle 3 Answers

2007-05-29T22:19:00.000-07:00

1)

Assume that contents of the container is X

On the first day 1/3rd is evaporated.
(1 - 1/3) of X is remaining i.e. (2/3)X

On the Second day 3/4th is evaporated. Hence,
(1- 3/4) of (2/3)X is remaining
i.e. (1/4)(2/3)X = (1/6) X

Hence 1/6th of the contents of the container is remaining

2)

Vipul studied for 3 hours in candle light.

Assume that the initial lenght of both the candle was L and Vipul studied for X hours.

In X hours, total thick candle burnt = XL/6
In X hours, total thin candle burnt = XL/4

After X hours, total thick candle remaining = L - XL/6
After X hours, total thin candle remaining = L - XL/4

Also, it is given that the thick candle was twice as long as the thin one when he finally went to sleep.
(L - XL/6) = 2(L - XL/4)
(6 - X)/6 = (4 - X)/2
(6 - X) = 3*(4 - X)
6 - X = 12 - 3X
2X = 6
X = 3

Hence, Vipul studied for 3 hours i.e. 180 minutes in candle light.

3)
Rs.333,062,500

To begin with, you want to know the total number of days: 365 x 50 = 18250.

By experimentation, the following formula can be discovered, & used to determine the amount earned for any particular day: 1 + 2(x-1), with x being the number of the day. Take half of the 18250 days, & pair them up with the other half in the following way: day 1 with day 18250, day 2 with day 18249, & so on, & you will see that if you add these pairs together, they always equal Rs.36500.

Multiply this number by the total number of pairs (9125), & you have the amount you would have earned in 50 years.

4)
Rs.22176

Assume his salary was Rs. X

He earns 5% raise. So his salary is (105*X)/100

A year later he receives 2.5% cut. So his salary is ((105*X)/100)*(97.5/100) which is Rs. 22702.68

Hence, solving equation ((105*X)/100)*(97.5/100) = 22702.68
X = 22176

5)

66 seconds

It is given that the time between first and last ticks at 6'o is 30 seconds.
Total time gaps between first and last ticks at 6'o = 5
(i.e. between 1 & 2, 2 & 3, 3 & 4, 4 & 5 and 5 & 6)

So time gap between two ticks = 30/5 = 6 seconds.

Now, total time gaps between first and last ticks at 12'o = 11
Therefore time taken for 12 ticks = 11 * 6 = 66 seconds (and not 60 seconds)

6)

There are 7 members in Mr. Mehta's family. Mother & Father of Mr. Mehta, Mr. & Mrs. Mehta, his son and two daughters.

Mother & Father of Mr. Mehta
|
Mr. & Mrs. Mehta
|
One Son & Two Daughters

7)

The soldier said, "You will put me to the sword."

The soldier has to say a Paradox to save himself. If his statement is true, he will be hanged, which is not the sword and hence false. If his statement is false, he will be put to the sword, which will make it true. A Paradox !!!

8)

As given, the person wanted to withdraw 100X + Y paise.

But he got 100Y + X paise.

After spending 20 paise, he has double the amount he wanted to withdraw. Hence, the equation is

2 * (100X + Y) = 100Y + X - 20

200X + 2Y = 100Y +X - 20

199X - 98Y = -20

98Y - 199X = 20

Now, we got one equation; but there are 2 variables. We have to apply little bit of logic over here. We know that if we interchange X & Y, amount gets double. So Y should be twice of X or one more than twice of X i.e. Y = 2X or Y = 2X+1

Case I : Y=2X
Solving two equations simultaneously
98Y - 199X = 20
Y - 2X = 0
We get X = - 20/3 & Y = - 40/2

Case II : Y=2X+1
Solving two equations simultaneously
98Y - 199X = 20
Y - 2X = 1
We get X = 26 & Y = 53

Now, its obvious that he wanted to withdraw Rs. 26.53

9)

Statement (4) is false. There are 3 men, 8 women and 6 children.

Assume that Statements (4), (5) and (6) are all true. Then, Statement (1) is false. But then Statement (2) and (3) both can not be true. Thus, contradictory to the fact that exactly one statement is false.

So Statement (4) or Statement (5) or Statement (6) is false. Also, Statements (1), (2) and (3) all are true.

From (1) and (2), there are 11 men and women. Then from (3), there are 2 possible cases - either there are 8 men and 3 women or there are 3 men and 8 women.

If there are 8 men and 3 women, then there is 1 child. Then Statements (4) and (5) both are false, which is not possible.

Hence, there are 3 men, 8 women and 6 children. Statement (4) is false.

10)

42% houses do not have tubelight, bulb and fan.

Let's assume that there are 100 houses. Hence, there should be total 300 items i.e. 100 tubelights, 100 bulbs and 100 fans.

From the given data, we know that there is shortage of atleast (67+83+73) 223 items in every 100 houses.

Also, exactly 19 houses do not have just one item. It means that remaining 81 houses should account for the shortage of remaining (223-19) 204 items. If those remaining 81 houses do not have 2 items each, there would be a shortage of 162 items. But total of 204 items are short. Hence, atleast (204-162) 42 houses do not have all 3 items - tubelight, bulb and fan.

Thus, 42% houses do not have tubelight, bulb and fan.

11)
The individual student should pay Rs. 50 for their journey.

Note that 3 persons are travelling between Bandra and Colaba.

The entire trip costs Rs. 300 to Mr. Subramanian. Hence, half of the trip costs Rs. 150.

For Andheri-Bandra-Andheri, only one person i.e. Mr. Subramaniam is travelling. Hence, he would pay Rs. 150.

For Bandra-Colaba-Bandra, three persons i.e Mr. Subramaniam and two students, are travelling. Hence, each student would pay Rs. 50.

12)

You are able to swim downstream at 3 miles an hour, & upstream at 2 miles an hour. There is a difference of 1 mile an hour, which is the river helping you in 1 direction, & slowing you in the other direction.

Average the 2 rates, & you have the rate that you can swim in still water, which is 2.5 miles an hour.

You can thus swim a mile in still water in 24 minutes.

13)
There are 1024 different ways.

This is the type of Brain Teaser that can be solved using the method of induction.

If there is just a one person and one seat, that person has only one option.

If there are two persons and two seats, it can be accomplished in 2 different ways.

If there are three persons and three seats, it can be accomplished in 4 different ways. Remember that no person can take a seat that separates him/her from at least one other person.

Similarly, four persons and four seats produce 8 different ways. And five persons with five seats produce 16 different ways.

It can be seen that with each additional person and seat, the different ways increase by the power of two. For six persons with six seats, there are 32 different ways.

For any number N, the different possible ways are 2 ^ (N-1)

Thus, for 11 persons and 11 seats, total different ways are 2 ^ 10 i.e. 1024

14)

Assume there are 6X boys and 4X Girls

Total Students taking lunch in canteen
= (6X)(60/100) + (4X)(40/100)
= 36(X/10) + 16(X/10)
= 52(X/10)

Total students are = 6X + 4X = 10X

% of class taking lunch in canteen
= ((52X/10) * 100 ) / 10X
= 52 %

15)

The Club originally had 24 members.

Assume that there were initially N members.

As 4 members resigned and remaining members paid Rs 26 each, it means that total amount of 4 members is equal to Rs 26 each from remaining (N-4) members. Thus,

4 * (3120 / N) = 26 * (N - 4)
12480 = 26N2 - 104N
26N2 - 104N - 12480 = 0

Solving the quadratic equation we get N=24.

Hence, the Club originally had 24 members.

16)
The tank will be full in 16 minutes.

In one minute,
pipe A can fill 1/30 part of the tank.
pipe B can fill 1/24 part of the tank.
pipe C can empty 1/80 part of the tank.

Thus, the net water level in one minute is
= 1/30 + 1/24 - 1/80
= 15/240 part of the tank

Hence, the tank will be full in 240/15 i.e. 16 minutes.

17)

The old man temporarily added his camel to the 17, making a total of 18 camels.

First son got 1/2 of it = 9

Second son got 1/3 of it = 6

Third son got 1/9 of it = 2

For a total of 17. He then takes his camel back and rides away......

18)

Blue box contains the maximum amount Rs. 40000

As it is given that only one of the given 3 statements is true; assume in turn, each statement to be true & the other 2 false and check whether the corresponding box contains the maximum amount.

Let's assume that the statement on the Blue box is true. Thus, the given 3 statements can be interpreted as
* Atmost one, a red box or a blue box contains Rs. 10000.
* Atmost one, a green box or a red box contains Rs. 25000.
* Both, a blue box and a green box contain Rs. 15000 each.

Going through all possible combinations, we can conclude that
Red Box : Rs. 10000 + Rs. 25000 = Rs. 35000
Green Box : Rs. 10000 + Rs. 15000 = Rs. 25000
Blue Box : Rs. 15000 + Rs. 25000 = Rs. 40000

You can test out for other two statements i.e. assuming Red box statement true and then Green box statement true. In both the cases, other statements will contradict the true statement.

19)

achin, Dravid and Ganguly scored 75, 87 and 78 respectively.

Sachin's score must be less than 86, otherwise Dravid's score would be more than 99. Also, he must have scored atleast 42 - incase Dravid and Ganguly scored 99 each.

Also, as none of them scored more than 99 and the total runs scored by them is 240; their individual scores must be around 80.

20)

A tough one.

It is obvious that C=1. Also, the maximum possible value of E is 7. Now, start putting possible values of D, E and R as they occure frequently and use trial-n-error.

W O R L D 5 3 6 8 4

+ T R A D E + 7 6 0 4 2

--- ---

C E N T E R 1 2 9 7 2 6

21)

7.5 degrees

At 3:15 minute hand will be perfactly horizontal pointing towards 3. Whereas hour hand will be towards 4. Also, hour hand must have covered 1/4 of angle between 3 and 4.

The angle between two adjacent digits is 360/12 = 30 degrees.

Hence 1/4 of it is 7.5 degrees.

22)

1, 2, 4, 8, 16, 32, 64, 128, 256, 489

Let's start from scratch.

The apple vandor can ask for only 1 apple, so one box must contain 1 apple.

He can ask for 2 apples, so one box must contain 2 apples.
He can ask for 3 apples, in that case box one and box two will add up to 3.

He can ask for 4 apples, so one box i.e. third box must contain 4 apples.

Now using box number one, two and three containing 1, 2 and 4 apples respectively, his son can give upto 7 apples. Hence, forth box must contain 8 apples.

Similarly, using first four boxes containing 1, 2, 4 and 8 apples, his son can give upto 15 apples. Hence fifth box must contain 16 apples.

You must have noticed one thing till now that each box till now contains power of 2 apples. Hence the answer is 1, 2, 4, 8, 16, 32, 64, 128, 256, 489. This is true for any number of apples, here in our case only upto 1000.

23)

The sequence of letters from the lowest value to the highest value is TUSQRPV.

From (3), Q is the middle term.
___ ___ ___ _Q_ ___ ___ ___

From (4), there must be exactly 2 numbers between P and S which gives two possible positions.

[1] ___ _S_ ___ _Q_ _P_ ___ ___

[2] ___ ___ _S_ _Q_ ___ _P_ ___

From (1), the number of letters between U and Q must be same as the number of letters between S and R. Also, the number of letters between them can be 1, 2 or 3.

Using trial and error, it can be found that there must be 2 letters between them. Also, it is possible only in option [2] above.

[2] ___ _U_ _S_ _Q_ _R_ _P_ ___

From (2) V must be the highest and the remaining T must be the lowest number.

_T_ _U_ _S_ _Q_ _R_ _P_ _V_

Thus, the sequence of letters from the lowest value to the highest value is TUSQRPV.

A contractor had employed 100 labourers for a flyover construction task. He did not allow any woman to work without her husband. Also, atleast half the men working came with their wives.
he sequence of letters from the lowest value to the highest value?

24)

16 men, 12 women and 72 children were working with the constructor.

Let's assume that there were X men, Y women and Z children working with the constructor. Hence,

X + Y + Z = 100
5X + 4Y + Z = 200

Eliminating X and Y in turn from these equations, we get
X = 3Z - 200
Y = 300 - 4Z

As if woman works, her husband also works and atleast half the men working came with their wives; the value of Y lies between X and X/2. Substituting these limiting values in equations, we get

if Y = X,
300 - 4Z = 3Z - 200
7Z = 500
Z = 500/7 i.e. 71.428

if Y = X/2,
300 - 4Z = (3Z - 200)/2
600 - 8Z = 3Z - 200
11Z = 800
Z = 800/11 i.e. 72.727

But Z must be an integer, hence Z=72. Also, X=16 and Y=12

There were 16 men, 12 women and 72 children working with the constructor.

25)13 not 12

He makes 9 originals from the 27 butts he found, and after he smokes them he has 9 butts left for another 3 cigars. And then he has 3 butts for another cigar.

So 9+3+1=13

26)

Cruz is Tanya's date.

As no two of them have the same number of preferred traits - from (1), exactly one of them has none of the preferred traits and exactly one of them has all the preferred traits.

From (4) and (5), there are only two possibilities:
* Adam & Cruz both are tall and Bond & Dumbo both are fair.
* Adam & Cruz both are short and Bond & Dumbo both are dark.

But from (2), second possibility is impossible. So the first one is the correct possibility i.e. Adam & Cruz both are tall and Bond & Dumbo both are fair.

Then from (3), Bond is short and handsome.

Also, from (1) and (2), Adam is tall and fair. Also, Dumbo is the person without any preferred traits. Cruz is Dark. Adam and Cruz are handsome. Thus, following are the individual preferred traits:

Cruz - Tall, Dark and Handsome
Adam - Tall and Handsome
Bond - Handsome
Dumbo - None :-(

Hence, Cruz is Tanya's date.

Consider a game of Tower of Hanoi

27)

There are number of ways to find the answer.

To move the largest disc (at level N) from one tower to the other, it requires 2(N-1) moves. Thus, to move N discs from one tower to the other, the number of moves required is
= 2^(N-1) + 2^(N-2) + 2^(N-3) + ..... + 2^2 + 2^1 + 2^0
= 2^N - 1

For N discs, the number of moves is one more than two times the number of moves for N-1 discs. Thus, the recursive function is
F(1) = 1
F(N) = 2*[F(N-1)] + 1
where N is the total number of discs

Also, one can arrive at the answer by finding the number of moves for smaller number of discs and then derive the pattern.
For 1 disc, number of moves = 1
For 2 discs, number of moves = 3
For 3 discs, number of moves = 7
For 4 discs, number of moves = 15
For 5 discs, number of moves = 31

Thus, the pattern is 2^N – 1

A boy found that he had a 48 inch strip of paper. He could cut an inch off every second.

28)
47 seconds.

To get 48 pieces, the boy have to put only 47 cuts. i.e. he can cut 46 pieces in 46 seconds. After getting 46 pieces, he will have a 2 inches long piece. He can cut it into two with just a one cut in 1 second. Hence, total of 47 seconds.

29)
A simple one. Use the given facts and put down all the players in order. The order is as follow with Harbhajan, the highest scorer and Laxman, the lowest scorer.

Harbhajan

Ganguly

Dravid

Badani, Agarkar

Sachin

Laxman

Also, as the lowest score was 10 runs. Laxman must have scored 10, Sachin 20, Badani & Agarkar 30 and so on.

Harbhajan - 60 runs

Ganguly - 50 runs

Dravid - 40 runs

Badani, Agarkar - 30 runs each

Sachin - 20 runs

Laxman - 10 runs

*******END OF ANSWER SESSION FOR PRACTISE PUZZLES - 3 *******

Thanks,
All the Best

Practice Puzzle 2 Answers

2007-05-29T22:18:00.002-07:00

1)

The required number is 236 and the sum is 11.

It is given that the first two digits of the required number are prime numbers i.e. 2, 3, 5 or 7. Note that 1 is neither prime nor composite. Also, the third digit is the multiplication of the first two digits. Thus, first two digits must be either 2 or 3 i.e. 22, 23, 32 or 33 which means that there are four possible numbers - 224, 236, 326 and 339.

Now, it is also given that - the difference between it's reverse and itself is 396. Only 236 satisfies this condition. Hence, the sum of the three digits is 11.

2)

A=2, B=1, C=9, D=4, E=3, F=8, G=6, H=5, I=7

Let's start with GHI = 9 * IE. Note that I appears on both the side. Also, after multiplying IE by 9 the answer should have I at the unit's place. The possible values of IE are 19, 28, 37, 46, 55, 64, 73, 82 and 91; out of which only 64, 73 and 82 satisfies the condition. (as all alphabet should represent different digits)

Now, consider DEF = 6 * IE. Out of three short-listed values, only 73 satisfies the equation. Also, ABC = 3 * IE is satisfied by 73.

Hence, A=2, B=1, C=9, D=4, E=3, F=8, G=6, H=5, I=7

219 438 657

--- = 73 --- = 73 --- = 73

3 6

3)

A, B & D are males; C is female. B is C's only son. A & D are C's brothers.

A(male) --- C(female) --- D(male)

|

|

B(male)

Work out which relation can hold and discard the contradictory options.

From (2) and (4), D can not be a only daughter and have a sister (B or C). Hence, D is A's brother i.e. D is a Male.

From (4), let's say that B is D's sister i.e. B is Female.
From (3), A is C's only son i.e. A is Male.
But D is A's brother which means that A is not C's only son. Hence, our assumption was wrong.

Thus, C is D's sister i.e. C is Female. And B must be C's only son.

Now it is clear that D & B are Males and C is Female. A must be a Male as only one of them is of opposite sex from each of the other three. And he is C & D's brother.How are they related to each other?

4)

32 minutes 43.6 seconds

In twelve hours, the minute hand and the hour hand are together for 11 times. It means that after every 12/11 hours, both the hands are together.

Similarly in twelve hours, the minute hand and the hour hand are exactly opposite to each other for 11 times. It means that after every 12/11 hours, both the hands are opposite.

Now, let's take an example. We know that at 12 both the hands are together and at 6 both the hands are exactly opposite to each other.

After 6, both the hands are in opposition at [6+(12/11)] hours, [6+2*(12/11)] hours, [6+3*(12/11)] hours and so on. The sixth such time is [6+6*(12/11)] hours which is the first time after 12. Thus after 12, both the hands are opposite to each other at 12:32:43.6

Hence, Dr. DoLittle takes 32 minutes and 43.6 seconds to reach home from the clinic.

5)

Mr. Haani crossed 7 SlowRun Expresses during his journey.

Let's say that Mr. Haani travelled by SlowRun Express on Wednesday 10:00PM from Mumbai. The first train he would have crossed is the one scheduled to arrive at Mumbai at 11:30 PM the same day i.e. the one that left Bangalore at 10:00 PM on last Sunday.

Also, he would have crossed the last train just before reaching Bangalore on Saturday.

6)

The cabins from left to right (1-6) are of Mr. Solanki, Mr. Sinha, Mr. Shaan, Mr. Sharma, Miss Shudha and Miss Shalaka.

From (2), cabin number 5 is assigned to Miss Shudha.

As Miss Shudha is allergic to smoke and Mr. Sinha, Mr. Shaan & Mr. Solanki all smoke, they must be in cabin numbers 1, 2 and 3 not necessarily in the same order. Also, Miss Shalaka and Mr. Sharma must be in cabin 4 and 6.

From (3), Mr. Shaan must be in cabin 3 and Mr. Sharma must be in cabin 4. Thus, Miss Shalaka is in cabin 6.

As Mr. Solanki needs silence during work and Mr. Shaan is in cabin 3 who often talks to Mr. Sharma during work, Mr. Solanki must be in cabin 1. Hence, Mr. Sinha is in cabin 2.

Thus, the cabins numbers are
1# Mr. Solanki,
2# Mr. Sinha,
3# Mr. Shaan,
4# Mr. Sharma,
5# Miss Shudha,
6# Miss Shalaka

7)

It is given that
2 wixsomes = 3 changs
8 wixsomes = 12 changs ----- (I)

Also, given that
4 changs = 1 plut
12 changs = 3 plutes
8 wixsomes = 3 plutes ----- From (I)

Therefore,
6 plutes = 16 wixsomes

8)

The required number is 236 and the sum is 11.

It is given that the first two digits of the required number are prime numbers i.e. 2, 3, 5 or 7. Note that 1 is neither prime nor composite. Also, the third digit is the multiplication of the first two digits. Thus, first two digits must be either 2 or 3 i.e. 22, 23, 32 or 33 which means that there are four possible numbers - 224, 236, 326 and 339.

Now, it is also given that - the difference between it's reverse and itself is 396. Only 236 satisfies this condition. Hence, the sum of the three digits is 11.

9)

A simple one.

As it is given that only one of the four statement is correct, the correct number can not appear in more than one statement. If it appears in more than one statement, then more than one statement will be correct.

Hence, there are 4 marbles under each mug.

10)

aswer is 7

11)

The cicumference of the earth is
= 2 * PI * r
= 2 * PI * 6400 km
= 2 * PI * 6400 * 1000 m
= 2 * PI * 6400 * 1000 * 100 cm
= 1280000000 * PI cm

where r = radius of the earth, PI = 3.141592654

Hence, the length of the thread is = 1280000000 * PI cm

Now length of the thread is increasd by 12 cm. So the new length is = (1280000000 * PI) + 12 cm

This thread will make one concentric circle with the earth which is slightly away from the earth. The circumfernce of that circle is nothing but (1280000000 * PI) + 12 cm

Assume that radius of the outer circle is R cm
Therefore,
2 * PI * R = (1280000000 * PI) + 12 cm

Solving above equation, R = 640000001.908 cm
Radius of the earth is r = 640000000 cm

Hence, the thread will be separatedfrom the earth by
= R - r cm
= 640000001.908 - 640000000
= 1.908 cm

12)
At the beginning of the 11th year, there would be 1,024,000 rabbits.

At the beginning, there were 1000 rabbits. Also, there were 4000 rabbits at the beginning of third year which is equal to 2828Z. Thus, Z = 4000/2828 i.e. 1.414 (the square root of 2)

Note that 2828Z can be represented as 2000*Z*Z (Z=1.414), which can be further simplified as 1000*Z*Z*Z*Z

Also, it is given that at the end of 6 months, there were 1000Z rabbits.

It is clear that the population growth is 1.414 times every six months i.e. 2 times every year. After N years, the population would be 1000*(Z^(2N)) i.e. 1000*(2^N)

Thus, at the beginning of the 11th year (i.e. after 10 years), there would be 1000*(2^10) i.e. 1,024,000 rabbits.

13)
The man drunk 190oz of water.

It is given that the man has 20oz bottle of sprite. Also, he will drink 1oz on the first day and refill the bottle with water, will drink 2oz on the second day and refill the bottle, will drink 3oz on the third day and refill the bottle, and so on till 20th day. Thus at the end of 20 days, he must have drunk (1 + 2 + 3 + 4 + ..... +18 + 19 + 20) = 210oz of liquid.

Out of that 210oz, 20oz is the sprite which he had initially. Hence, he must have drunk 190oz of water.ed

14)
There are 5 such expressions.

99 + (9/9) = 100

(99/.99) = 100

(9/.9) * (9/.9) = 100

((9*9) + 9)/.9 = 100

(99-9)/.9 = 100

15)

answer is 7/9

Assume that number of boys graduated from City High School = B
Therefore, number of girls graduated from City High School = 2*B

It is given that 3/4 of the girls and 5/6 of the boys went to college immediately after graduation.
Hence, total students went to college
= (3/4)(2*B) + (5/6)(B)
= B * (3/2 + 5/6)
= (7/3)B

Fraction of the graduates that year went to college immediately after graduation
= [(7/3)B] / [3*B]
= 7/9

Therefore, the answer is 7/9

16)

The mule was carrying 5 sacks and the donkey was carrying 7 sacks.

Let's assume that the mule was carrying M sacks and the donkey was carrying D sacks.

As the donkey told the mule, "If you gave me one of your sacks I'd have double what you have."
D + 1 = 2 * (M-1)
D + 1 = 2M - 2
D = 2M - 3

The donkey also said, "If I give you one of my sacks we'd have an even amount."
D - 1 = M + 1
D = M + 2

Comparing both the equations,
2M - 3 = M + 2
M = 5

Substituting M=5 in any of above equation, we get D=7

Hence, the mule was carrying 5 sacks and the donkey was carrying 7 sacks.

17) Person A came in first.

Let's assume that the distance between start and the point is D miles.

Total time taken by Person A to finish
= (D/20) + (D/20)
= D/10
= 0.1D

Total time taken by Person B to finish
= (D/10) + (D/30)
= 2D/15
= 0.1333D

Thus, Person A is the Winner.

18)

Assume that initial there were 3*X bullets.

So they got X bullets each after division.

All of them shot 4 bullets. So now they have (X - 4) bullets each.

But it is given that, after they shot 4 bullets each, total number of bullets remaining is equal to the bullets each had after division i.e. X

Therefore, the equation is
3 * (X - 4) = X
3 * X - 12 = X
2 * X = 12
X = 6

Therefore the total bullets before division is = 3 * X = 18

19)The sum of the digits of D is 1.

Let E = sum of digits of D.

It follows from the hint that A = E (mod 9)

consider, (" ^ " means power)
A = 1999 ^ 1999
< 2000 ^ 2000
= 2 ^ 2000 * 1000 ^ 2000
= 1024 ^ 200 * 10 ^ 6000

< 10 ^ 800 * 10 ^ 6000

= 10 ^ 6800

i.e. A < 106800

i.e. B < 6800 * 9 = 61200

i.e. C < 5 * 9 = 45

i.e. D < 2 * 9 = 18

i.e. E <= 9

i.e. E is a single digit number.

Also,

1999 = 1 (mod 9)

so 19991999 = 1 (mod 9)

Therefore we conclude that E=1.

20)

The last person covered 120.71 meters.

It is given that the platoon and the last person moved with uniform speed. Also, they both moved for the identical amount of time. Hence, the ratio of the distance they covered - while person moving forward and backword - are equal.

Let's assume that when the last person reached the first person, the platoon moved X meters forward.

Thus, while moving forward the last person moved (50+X) meters whereas the platoon moved X meters.

Similarly, while moving back the last person moved [50-(50-X)] X meters whereas the platoon moved (50-X) meters.

Now, as the ratios are equal,
(50+X)/X = X/(50-X)
(50+X)*(50-X) = X*X

Solving, X=35.355 meters

Thus, total distance covered by the last person
= (50+X) + X
= 2*X + 50
= 2*(35.355) + 50
= 120.71 meters

Note that at first glance, one might think that the total distance covered by the last person is 100 meters, as he ran the total length of the platoon (50 meters) twice. TRUE, but that's the relative distance covered by the last person i.e. assuming that the platoon is stationary.

21) answer is 9

To verify this, you can make a drawing of a cube, & number each of its 12 edges. Then, always starting from 1 corner & 1 edge, you can determine all of the possible combinations for tracing along the edges of a cube.

There is no need to start from other corners or edges of the cube, as you will only be repeating the same combinations. The process is a little more involved than this, but

is useful for solving many types of spatial puzzles.

22)

Mr. Bajaj is the Engineer and either his wife or his son is the Doctor.

Mr. Bajaj's wife and mother are not blood relatives. So from 3, if the Engineer is a female, the Doctor is a male. But from 1, if the Doctor is a male, then the Engineer is a male. Thus, there is a contradiction, if the Engineer is a female. Hence, either Mr. Bajaj or his son is the Engineer.

Mr. Bajaj's son is the youngest of all four and is blood relative of each of them. So from 2, Mr. Bajaj's son is not the Engineer. Hence, Mr. Bajaj is the Engineer.

Now from 2, Mr. Bajaj's mother can not be the Doctor. So the Doctor is either his wife or his son . It is not possible to determine anything further.

23)

Carrie is married to Cam.

"Sam's wife and Billy's Husband play Carrie and Tina's husband at bridge."

It means that Sam is not married to either Billy or Carrie. Thus, Sam is married to Tina.

As Cam does not play bridge, Billy's husband must be Laurie.

Hence, Carrie is married to Cam

24)

One way to solve it is by making 3 equations and solve them simultaneously. But there is rather easier way to solve it using Backtracing.

It's given that at the end, each had 24 tractors (24, 24, 24) i.e. after Z gave tractors to X & Y as many as they had. It means that after getting tractors from Z their tractors got doubled. So before Z gave them tractors, they had 12 tractors each and Z had 48 tractors. (12, 12, 48)

Similarly, before Y gave tractors to X & Z, they had 6 & 24 tractors respectively and Y had 42 tractors i.e. (6, 42, 24)

Again, before X gave tractors to Y & Z, they had 21 & 12 tractors respectively and X had 39 tractors i.e. (39, 21, 12)

Hence, initially X had 39 tractors, Y had 21 tractors and Z had 12 tractors.

25)

The sign-maker will need 192 zeroes.

Divide 1000 building numbers into groups of 100 each as follow:
(1..100), (101..200), (201..300), ....... (901..1000)

For the first group, sign-maker will need 11 zeroes.
For group numbers 2 to 9, he will require 20 zeroes each.
And for group number 10, he will require 21 zeroes.

The total numbers of zeroes required are
= 11 + 8*20 + 21
= 11 + 160 + 21
= 192

26)

It is always possible to find odd coin in 3 weighings and to tell whether the odd coin is heavier or lighter.

Take 8 coins and weigh 4 against 4.

If both are not equal, goto step 2

If both are equal, goto step 3

One of these 8 coins is the odd one. Name the coins on heavier side of the scale as H1, H2, H3 and H4. Similarly, name the coins on the lighter side of the scale as L1, L2, L3 and L4. Either one of H's is heavier or one of L's is lighter. Weigh (H1, H2, L1) against (H3, H4, X) where X is one coin remaining in intial weighing.

If both are equal, one of L2, L3, L4 is lighter. Weigh L2 against L3.

If both are equal, L4 is the odd coin and is lighter.

If L2 is light, L2 is the odd coin and is lighter.

If L3 is light, L3 is the odd coin and is lighter.

If (H1, H2, L1) is heavier side on the scale, either H1 or H2 is heavier. Weight H1 against H2

If both are equal, there is some error.

If H1 is heavy, H1 is the odd coin and is heavier.

If H2 is heavy, H2 is the odd coin and is heavier.

If (H3, H4, X) is heavier side on the scale, either H3 or H4 is heavier or L1 is lighter. Weight H3 against H4

If both are equal, L1 is the odd coin and is lighter.

If H3 is heavy, H3 is the odd coin and is heavier.

If H4 is heavy, H4 is the odd coin and is heavier.

The remaining coin X is the odd one. Weigh X against the anyone coin used in initial weighing.

If both are equal, there is some error.

If X is heavy, X is the odd coin and is heavier.

If X is light, X is the odd coin and is lighter.

27)

Total 36 medals were awarded and the contest was for 6 days.

On day 1: Medals awarded = (1 + 35/7) = 6 : Remaining 30 medals
On day 2: Medals awarded = (2 + 28/7) = 6 : Remaining 24 medals
On day 3: Medals awarded = (3 + 21/7) = 6 : Remaining 18 medals
On day 4: Medals awarded = (4 + 14/7) = 6 : Remaining 12 medals
On day 5: Medals awarded = (5 +7/7) = 6 : Remaining 6 medals
On day 6: Medals awarded 6

I got this answer by writing small program. If anyone know any other simpler method, do submit it.

28)

The answer is 381654729

One way to solve it is Trial-&-Error. You can make it bit easier as odd positions will always occupy ODD numbers and even positions will always occupy EVEN numbers. Further 5th position will contain 5 as 0 does not occur.

The other way to solve this problem is by writing a computer program that systematically tries all possibilities

***********************************ENF OF ANSWER SESSION FOR PRACTISE PUZZLES - 2 ***************************

Thanks,
All The Best

Practice Puzzle 1 Answers

2007-05-29T22:18:00.001-07:00

)
6,48,64,800 ways

There are total 16 pieces which can be arranged on 16 places in 16P16 = 16! ways.
(16! = 16 * 15 * 14 * 13 * 12 * ..... * 3 * 2 * 1)

But, there are some duplicate combinations because of identical pieces.

There are 8 identical pawn, which can be arranged in 8P8 = 8! ways.

Similarly there are 2 identical rooks, 2 identical knights and 2 identical bishops. Each can be arranged in 2P2 = 2! ways.

Hence, the require answer is
= (16!) / (8! * 2! * 2! * 2!)
= 6,48,64,800

2)
Rs. 250/-

Assume that initially he had Rs. X
He spent 1/3 for cloths =. (1/3) * X
Remaining money = (2/3) * X

He spent 1/5 of remaining money for food = (1/5) * (2/3) * X = (2/15) * X
Remaining money = (2/3) * X - (2/15) * X = (8/15) * X

Again, he spent 1/4 of remaining maoney for travel = (1/4) * (8/15) * X = (2/15) * X
Remaining money = (8/15) * X - (2/15) * X = (6/15) * X

But after spending for travel he is left with Rs. 100/- So
(6/15) * X = 100
X = 250

3)

20 cows

g - grass at the beginning
r - rate at which grass grows, per day
y - rate at which one cow eats grass, per day
n - no of cows to eat the grass in 96 days

From given data,
g + 24*r = 70 * 24 * y - A
g + 60*r = 30 * 60 * y - B
g + 96*r = n * 96 * y - C

Solving for (B-A),
(60 * r) - (24 * r) = (30 * 60 * y) - (70 * 24 * y)
36 * r = 120 * y - D

Solving for (C-B),
(96 * r) - (60 * r) = (n * 96 * y) - (30 * 60 * y)
36 * r = (n * 96 - 30 * 60) * y
120 * y = (n * 96 - 30 * 60) * y [From D]
120 = (n * 96 - 1800)
n = 20

Hence, 20 cows are needed to eat the grass in 96 days.

4)

65292

As per given conditions, there are three possible combinations for 2nd, 3rd and 4th digits. They are (3, 0, 7) or (4, 1, 8) or (5, 2, 9)

It is given that there are 3 pairs whose sum is 11. All possible pairs are (2, 9), (3, 8), (4, 7), (5, 6). Now required number is 5 digit number and it contains 3 pairs of 11. So it must not be having 0 and 1 in it. Hence, the only possible combination for 2nd, 3rd and 4th digits is (5, 2, 9)

Also, 1st digit is thrice the last digit. The possible combinations are (3, 1), (6, 2) and (9, 3), out of which only (6, 2) with (5, 2, 9) gives 3 pairs of 11. Hence, the answer is 65292.

5)
The answer is 285714.

If its rightmost digit is placed at its left end, then new number is 428571 which is 50% larger than the original number 285714

The simplest way is to write a small program. And the other way is trial and error !!!

6)

52 / 2703

There are two cases to be considered.

CASE 1 : King of Hearts is drawn from Pack A and shuffled with Pack B

Probability of drawing King of Hearts from Pack A = 1/51 (as Queen of Hearts is not to be drawn)
Probability of having King of Hearts on the top of the Pack B = 2/53

So total probability of case 1 = (1/51) * (2/53) = 2 / (51 * 53)

CASE 2 : King of Hearts is not drawn from Pack A

Probability of not drawing King of Hearts from Pack A = 50/51 (as Queen of Hearts is not to be drawn)
Probability of having King of Hearts on the top of the Pack B = 1/53

So total probability of case 2 = (50/51) * (1/53) = 50 / (51 * 53)

Now adding both the probability, the required probability is
= 2 / (51 * 53) + 50 / (51 * 53)
= 52 / (51 * 53)
= 52 / 2703
= 0.0192378

7)
The maximum number of attempts required are 16,22,400

There are 52 possible letters - a to z and A to Z, and 10 possible numbers - 0 to 9. Now, 4 characters - 2 letters and 2 numbers, can be selected in 52*52*10*10 ways. These 4 characters can be arranged in 4C2 i.e. 6 different ways - the number of unique patterns that can be formed by lining up 4 objects of which 2 are distinguished one way (i.e. they must be letters) and the other 2 are distinguished another way (i.e. they must be numbers).

Consider an example : Let's assume that @ represents letter and # represents number. the 6 possible ways of arranging them are : @@##, @#@#, @##@, #@@#, #@#@, ##@@

Hence, the required answer is
= 52*52*10*10*6
= 16,22,400 attempts
= 1.6 million approx.

8)
There are 4.3252 * 10^19 possible combinations for 3x3x3 Rubics and 7.4012 * 10^45 possible combinations for 4x4x4 Rubics.

Let's consider 3x3x3 Rubics first.

There are 8 corner cubes, which can be arranged in 8! ways.
Each of these 8 cubes can be turned in 3 different directions, so there are 3^8 orientations altogether. But if you get all but one of the corner cube into chosen positions and orientations, only one of 3 orientations of the final corner cube is possible. Thus, total ways corner cubes can be placed = (8!) * (3^8)/8 = (8!) * (3^7)

Similarly, 12 edge cubes can be arranged in 12! ways.
Each of these 12 cubes can be turned in 2 different directions, so there are 2^12 orientations altogether. But if you get all but one of the edge cube into chosen positions and orientations, only one of 2 orientations of the final edge cube is possible. Thus, total ways edge cubes can be placed = (12!) * (2^12)/2 = (12!) * (2^11)

Here, we have essentially pulled the cubes apart and stuck cubes back in place wherever we please. In reality, we can only move cubes around by turning the faces of the cubes. It turns out that you can't turn the faces in such a way as to switch the positions of two cubes while returning all the others to their original positions. Thus if you get all but two cubes in place, there is only one attainable choice for them (not 2!). Hence, we must divide by 2.

Total different possible combinations are
= [(8!) * (3^7)] * [(12!) * (2^11)] / 2
= (8!) * (3^7) * (12!) * (2^10)
= 4.3252 * 10^19

Similarly, for 4x4x4 Rubics total different possible combinations are
= [(8!) * (3^7)] * [(24!)] * [(24!) / (4!^6)] / 24
= 7.4011968 * 10^45

Note that there are 24 edge cubes, which you can not turn in 2 orientations (hence no 2^24 / 2). Also, there are 4 center cubes per face i.e. (24!) / (4!^6). You can switch 2 cubes without affecting the rest of the combination as 4*4*4 has even dimensions (hence no division by 2). But pattern on one side is rotated in 4 directions over 6 faces, hence divide by 24.

9)
Answer

A tough one!!!

Since R + E + E = 10 + E, it is clear that R + E = 10 and neither R nor E is equal to 0 or 5. This is the only entry point to

solve it. Now use trial-n-error method.

N E V E R 2 1 4 1 9

L E A V E 3 1 5 4 1

+ M E + 6 1

-------- --------

A L O N E 5 3 0 2 1

10)

Cindy is the Singer. Mr. Clinton or Monika is the Dancer.

From (1) and (3), the singer and the dancer, both can not be a man. From (3) and (4), if the singer is a man, then the dancer must be a man. Hence, the singer must be a woman.

CASE I : Singer is a woman and Dancer is also a woman
Then, the dancer is Monika and the singer is Cindy.

CASE II : Singer is a woman and Dancer is also a man
Then, the dancer is Mr. Clinton and the singer is Cindy.

In both the cases, we know that Cindy is the Singer. And either Mr. Clinton or Monika is the Dancer.

11)

There are total 450 rooms.

Out of which 299 room number starts with either 1, 2 or 3. (as room number 100 is not there) Now out of those 299 rooms only 90 room numbers end with 4, 5 or 6

So the probability is 90/450 i.e. 1/5 or 0.20

Draw 9 dots on a page, in the shape of three rows of three dots to form a square. Now place your pen on the page, draw 4 straight lines and try and cover all the dots.

You're not allowed to lift your pen.

Note: Don't be confined by the dimensions of the square.

12)

One way to solve it is by making 3 equations and solve them simultaneously. But there is rather easier way to solve it using Backtracing.

It's given that at the end, each had 24 tractors (24, 24, 24) i.e. after Z gave tractors to X & Y as many as they had. It means that after getting tractors from Z their tractors got doubled. So before Z gave them tractors, they had 12 tractors each and Z had 48 tractors. (12, 12, 48)

Similarly, before Y gave tractors to X & Z, they had 6 & 24 tractors respectively and Y had 42 tractors i.e. (6, 42, 24)

Again, before X gave tractors to Y & Z, they had 21 & 12 tractors respectively and X had 39 tractors i.e. (39, 21, 12)

Hence, initially X had 39 tractors, Y had 21 tractors and Z had 12 tractors.

13)

None

Frank gave you a pear in exchange of the apple which Marge gave you. And you gave that pear to Bret in exchange for an apple. All the others exchanges involved apples and/or organges.

Four couples are going to the movie. Each row holds eight seats. Betty and Jim don't want to sit next to Alice and Tom. Alice and Tom don't want to sit next to Gertrude and Bill. On the otherhand, Sally and Bob don't want to sit next to Betty and Jim.

14)

Let before adding X stations, total number of tickets
t = N(N-1)

After adding X stations total number of tickets are
t + 46 = (N+X)(N+X-1)

Subtracting 1st from 2nd
46 = (N+X)(N+X-1) - N(N-1)
46 = N2 + NX - N + NX + X2 - X - N2 + N
46 = 2NX + X2 - X
46 = (2N - 1)X + X2
X2 + (2N - 1)X - 46 = 0

Now there are only two possible factors of 46. They are (46,1) and (23,2)

Case I: (46,1)
2N - 1 = 45
2N = 46
N = 23
And X = 1

Case II: (23,2)
2N - 1 = 21
2N = 22
N = 11
And X = 2

Hence, there are 2 possible answers.

15)

75 miles per hour

While going to the destination, the vehicle travels 10 mils at the speed of 50 miles per hour. So the time taken to travel 10 miles is
= (60 * 10) / 50
= 12 minutes

Now it's given that round-trip travel time is 20 minutes. So the vehicle should complete its return trip of 10 miles in 8 minutes. So the speed of the vehicle must
= (60 * 10) / 8
= 75 miles per hour

16)

70 students are majoring in both, psychology & business

If 73% of the students are psychology majors, we know that 27% are not psychology majors. By the same reasoning, 38% are not business majors, because 62% of the students do major in business. So: 27 + 38 = 65

65% of the students are not majoring in both psychology & business, so 35% are double majors, a total of 70 students.

17)

Initially, there were 42 or 36 matches in the match-box.

There are 42 matches in the box with which he could form a triangle 20, 15, 7, with an area of 42 square inches. After 6 matches had been used, the remaining 36 matches would form a triangle 17, 10, 9, with an area of 36 square inches. After using another 6 matches, the remaining 30 matches would form a triangle 13, 12, 5, with an area of 30 square inches. After using another 6, the 24 remaining would form a triangle 10, 8, 6, with an area of 24 square inches.

Thus, there are two possible answers. There were either 42 or 36 matches in the match-box.

18)

Mr. Grey is wearing Black suit.
Mr. White is wearing Grey suit.
Mr. Black is wearing White suit.

Mr. Grey must not be wearing grey suit as that is the same colour as his name. Also, he was not wearing white suit as the person wearing white suit responded to his comment. So Mr Grey must be wearing a black suit.

Similarly, Mr. White must be wearing either black suit or grey suit. But Mr. Grey is wearing a black suit. Hence, Mr. White must be wearing a grey suit.

And, Mr. Black must be wearing white suit

******************************END OF ANSWERS FOR FIRST PRACTISE EXERCISE***********************************

thanks,
ALL THE BEST

Practice Puzzle 4

2007-05-29T22:17:00.001-07:00

1) Decipher this sentence.

B R W Q H L F K W H J K Q I B W K

Q I C E D W Z B G W K K M I K E

Z B G Q H S K Z B G J K Z K W

B U U Z B G J D B H F W.

2) At what time immediately prior to Six O'clock the hands of the clock are exactly opposite to each other. Give the exact time in hours, minutes and seconds

3) Ali Baba had four sons, to whom he bequeathed his 39 camels, with the proviso that the legacy be divided in the following way :

The oldest son was to receive one half the property, the next a quarter, the third an eighth and the youngest one tenth. The four brothers were at a loss as how to divide the inheritance among themselves without cutting up a camel, until a stranger appeared upon the scene.
Dismounting from his camel, he asked if he might help, for he knew just what to do. The brothers gratefully accepted his offer.

Adding his own camel to Ali Baba's 39, he divided the 40 as per the will. The oldest son received 20, the next 10, the third 5 and the youngest 4. One camel remained : this was his, which he mounted and rode away.

Scratching their heads in amazement, they started calculating. The oldest thought : is not 20 greater than the half of 39? Someone must have received less than his proper share ! But each brother discovered that he had received more than his due. How is it possible?

4) There is a family party consisting of two fathers, two mothers, two sons, one father-in-law, one mother-in-law, one daughter-in-law, one grandfather, one grandmother and one grandson.

What is the minimum number of persons required so that this is possible?

5) A man went into a fast food restaurant and ate a meal costing Rs. 105, giving the accountant a Rs. 500 note. He kept the change, came back a few minutes later and had some food packed for his girl friend. He gave the accountant a Rs. 100 note and received Rs. 20 in change. Later the bank told the accountant that both the Rs. 500 and the Rs. 100 notes were counterfeit.

How much money did the restaurant lose? Ignore the profit of the food restaurant.

6)
S L I D E

- D E A N

3 6 5 1

Each of seven digits from 0-9 are represented by a different letter above such that the subtraction is true.

What word represents 3651?

7) Adam, Burzin, Clark and Edmund each live in an apartment. Their apartments are arranged in a row numbered 1 to 4 from left to right. Also, one of them is the landlord.

If Clark's apartment is not next to Burzin's apartment, then the landlord is Adam and lives in apartment 1.

If Adam's apartment is right of Clark's apartment, then the landlord is Edmund and lives in apartment 4.

If Burzin's apartment is not next to Edmund's apartment, then the landlord is Clark and lives in apartment 3.

If Edmund's apartment is right of Adam's apartment, then the landlord is Burzin and lives in apartment 2.

Who is the landlord?

8) B, J and P are related to each other.

Among the three are B's legal spouse, J's sibling and P's sister-in-law.

B's legal spouse and J's sibling are of the same sex.

Who is the married man?

9) A cube is made of a white material, but the exterior is painted black.

If the cube is cut into 125 smaller cubes of exactly the same size, how many of the cubes will have atleast 2 of their sides painted black?

10) Imagine a triangle of coins on a table so that the first row has one coin in it and the second row has two coins in it and so on. If you can only move one coin at a time, how many moves does it take to make the triangle point the other way?

For a triangle with two row it is one, for a triangle with three rows it is two, for a triangle with four rows it is three.

For a traingle with five rows is it four?
11) A man is going to an Antique Car auction. All purchases must be paid for in cash. He goes to the bank and draws out $25,000.

Since the man does not want to be seen carrying that much money, he places it in 15 evelopes numbered 1 through 15. Each envelope contains the least number of bills possible of any available US currency (i.e. no two tens in place of a twenty).

At the auction he makes a successful bid of $8322 for a car. He hands the auctioneer envelopes number(s) 2, 8, and 14. After opening the envelopes the auctioneer finds exactly the right amount.

How many ones did the auctioneer find in the envelopes?

12) The minute and the hour hand of a watch meet every 65 minutes.

How much does the watch lose or gain time and by how much?

13) There is a number that is 5 times the sum of its digits. What is this number? Answer is not 0.

14) There are six boxes containing 5, 7, 14, 16, 18, 29 balls of either red or blue in colour. Some boxes contain only red balls and others contain only blue.

One sales man sold one box out of them and then he says, "I have the same number of red balls left out as that of blue."

Which box is the one he solds out?

15) Ekta got chocolates to give her friends on her Birthday. If she gives 3 chocolates to each friend, one friend will get only 2 chocolates. Also, if she gives 2 chocolates to each friends, she will left with 15 chocolates.

How many chocolates Ekta got on her Birthday? and how many friends are there?

16) Pooja and Esha met each other after long time. In the course of their conversation, Pooja asked Esha her age. Esha replied, "If you reverse my age, you will get my husbund's age. He is of course older than me. Also, the difference between our age is 1/11th of the sum of our age."

Can you help out Pooja in finding Esha's age?

17) A fish had a tail as long as its head plus a quarter the lenght of its body. Its body was three-quarters of its total length. Its head was 4 inches long.

What was the length of the fish?

18) Assume that you have just heard of a scandal and you are the first one to know. You pass it on to four person in a matter of 30 minutes. Each of these four in turn passes it to four other persons in the next 30 minutes and so on.

How long it will take for everybody in the World to get to know the scandal?

Assume that nobody hears it more than once and the population of the World is approximately 5.6 billions.

Practice Puzzle 3

2007-05-29T22:15:00.000-07:00

1) 1/3 rd of the contents of a container evaporated on the 1st day. 3/4th of the remaining contents of the container evaporated on the second day. What part of the contents of the container is left at the end of the second day?

2) Vipul was studying for his examinations and the lights went off. It was around 1:00 AM. He lighted two uniform candles of equal length but one thicker than the other. The thick candle is supposed to last six hours and the thin one two hours less. When he finally went to sleep, the thick candle was twice as long as the thin one.
For how long did Vipul study in candle light?

3) If you started a business in which you earned Rs.1 on the first day, Rs.3 on the second day, Rs.5 on the third day, Rs.7 on the fourth day, & so on.
How much would you have earned with this business after 50 years (assuming there are exactly 365 days in every year)?

Math gurus may use series formula to solve it.(series: 1,3,5,7,9,11.....upto 18250 terms)

4) A worker earns a 5% raise. A year later, the worker receives a 2.5% cut in pay, & now his salary is Rs. 22702.68

What was his salary to begin with?

5) At 6'o a clock ticks 6 times. The time between first and last ticks is 30 seconds. How long does it tick at 12'o.

6) In Mr. Mehta's family, there are one grandfather, one grandmother, two fathers, two mothers, one father-in-law, one mother-in-law, four children, three grandchildren, one brother, two sisters, two sons, two daughters and one daughter-in-law. How many members are there in Mr. Mehta's family? Give minimal possible answer.

7) When Alexander the Great attacked the forces of Porus, an Indian soldier was captured by the Greeks. He had displayed such bravery in battle, however, that the enemy offered to let him choose how he wanted to be killed. They told him, "If you tell a lie, you will put to the sword, and if you tell the truth you will be hanged."

The soldier could make only one statement. He made that statement and went free. What did he say?

8) A person wanted to withdraw X rupees and Y paise from the bank. But cashier made a mistake and gave him Y rupees and X paise. Neither the person nor the cashier noticed that.

After spending 20 paise, the person counts the money. And to his surprise, he has double the amount he wanted to withdraw.

Find X and Y. (1 Rupee = 100 Paise)

9) At the Party:

There were 9 men and children.

There were 2 more women than children.

The number of different man-woman couples possible was 24. Note that if there were 7 men and 5 women, then there would have been 35 man-woman couples possible.

Also, of the three groups - men, women and children - at the party:

There were 4 of one group.

There were 6 of one group.

There were 8 of one group.

Exactly one of the above 6 statements is false.

Can you tell which one is false? Also, how many men, women and children are there at the party

10) There is a shortage of tube lights , bulbs and fans in a village - Kharghar. It is found that

All houses do not have either tubelight or bulb or fan.

exactly 19% of houses do not have just one of these.

atleast 67% of houses do not have tubelights.

atleast 83% of houses do not have bulbs.

atleast 73% of houses do not have fans.

What percentage of houses do not have tubelight, bulb and fan?

11) Mr. Subramaniam rents a private car for Andheri-Colaba-Andheri trip. It costs him Rs. 300 everyday.

One day the car driver informed Mr. Subramaniam that there were two students from Bandra who wished to go from Bandra to Colaba and back to Bandra. Bandra is halfway between Andheri and Colaba. Mr. Subramaniam asked the driver to let the students travel with him.

On the first day when they came, Mr. Subramaniam said, "If you tell me the mathematically correct price you should pay individually for your portion of the trip, I will let you travel for free."

How much should the individual student pay for their journey?

12) In training for a competition, you find that swimming downstream (with the current) in a river, you can swim 2 miles in 40 minutes, & upstream (against the current), you can swim 2 miles in 60 minutes.

How long would it take you to swim a mile in still water?

13) How many different ways can this be accomplished? Note that the first person can choose any of the 11 seats.

(question is not completly avilable..will be updated asap)

14) The ratio of Boys to Girls is 6:4. 60% of the boys and 40% of the girls take lunch in the canteen. What % of class takes lunch in canteen?

15) In the General meeting of "Friends Club", Sameer said, "The repairs to the Club will come to a total of Rs 3120 and I propose that this amount should be met by the members, each paying an equal amount."

The proposal was immediately agreed. However, four members of the Club chose to resign, leaving the remaining members to pay an extra Rs 26 each.

How many members did the Club originally have?

16) A tank can be filled by pipe A in 30 minutes and by pipe B in 24 minutes. Outlet pipe C can empty the full tank in one hour and twenty minutes.

If the tank is empty initially and if all the three pipes A, B and C are opened simultaneously, in how much time will the tank be full?

17) A rich old Arab has three sons. When he died, he willed his 17 camels to the sons, to be divided as follows:

First Son to get 1/2 of the camels Second Son to get 1/3rd of the camels Third Son to get 1/9th of the camels.

The sons are sitting there trying to figure out how this can possibly be done, when a very old wise man goes riding by. They stop him and ask him to help them solve their problem. Without hesitation he divides the camels properly and continues riding on his way.

How did he do it?

18) There are 3 colored boxes - Red, Green and Blue. Each box contains 2 envelopes. Each envelope contains money - two of them contain Rs. 25000 each, two of them contain Rs. 15000 each and remaining two contain Rs. 10000 each.

There is one statement written on the cover of each box.
* Red Box: Both, a red box and a blue box contain Rs. 10000 each.
* Green Box: Both, a green box and a red box contain Rs. 25000 each.
* Blue Box: Both, a blue box and a green box contain Rs. 15000 each.

Only one of the above 3 statements is true and the corresponding box contains the maximum amount.

Can you tell which box contains the maximum amount and how much?

19) Sachin, Dravid and Ganguly played in a Cricket match between India and England.

None of them scored more than 99 runs.

If you add the digits of the runs scored by Sachin to his own score, you will get the runs scored by Dravid.

If you reverse the digits of the runs scored by Dravid, you will get the runs scored by Ganguly.

The total runs scored by them is 240.

Can you figure out their individual scores?

20) Substitute digits for the letters to make the following relation true.

W O R L D

+ T R A D E

----

C E N T E R

Note that the leftmost letter can't be zero in any word. Also, there must be a one-to-one mapping between digits and letters. e.g. if you substitute 3 for the letter W, no other letter can be 3 and all other W in the puzzle must be 3.

21) If you look at a clock and the time is 3:15.

What is the angle between the hour and the minute hands? ( The answer to this is not zero!)

22) An apple vendor has 1000 apples and 10 empty boxes. He asks his son to place all the 1000 apples in all the 10 boxes in such a manner that if he asks for any number of apples from 1 to 1000, his son should be able to pick them in terms of boxes.

How did the son place all the apples among the 10 boxes, given that any number of apples can be put in one box.

23) The letters P, Q, R, S, T, U and V, not necessarily in that order represents seven consecutive integers from 22 to 33.

U is as much less than Q as R is greater than S.

V is greater than U.

Q is the middle term.

P is 3 greater than S.

Can you find the sequence of letters from the lowest value to the highest value?

24) He paid five rupees per day to each man, four ruppes to each woman and one rupee to each child. He gave out 200 rupees every evening.

How many men, women and children were working with the constructor?

25) Because cigars cannot be entirely smoked, a Bobo who collects cigar butts can make a cigar to smoke out of every 3 butts that he finds.

Today, he has collected 27 cigar butts. How many cigars will he be able to smoke?

26) anya wants to go on a date and prefers her date to be tall, dark and handsome.

Of the preferred traits - tall, dark and handsome - no two of Adam, Bond, Cruz and Dumbo have the same number.

Only Adam or Dumbo is tall and fair.

Only Bond or Cruz is short and handsome.

Adam and Cruz are either both tall or both short.

Bond and Dumbo are either both dark or both fair.

Who is Tanya's date?

27)If the tower has 2 discs, the least possible moves with which you can move the entire tower to another peg is 3.

If the tower has 3 discs, the least possible moves with which you can move the entire tower to another peg is 7.

What is the least possible moves with which you can move the entire tower to another peg if the tower has N discs?

28) How long would it take for him to cut 48 pieces? He can not fold the strip and also, can not stack two or more strips and cut them together.

29) The cricket match between India and Pakistan was over.

Harbhajan scored more runs than Ganguly.

Sachin scored more runs than Laxman but less than Dravid

Badani scored as much runs as Agarkar but less than Dravid and more than Sachin.

Ganguly scored more runs than either Agarkar or Dravid.

Each batsman scored 10 runs more than his immediate batsman. The lowest score was 10 runs. How much did each one of them score

Practice Puzzle 2

2007-05-29T22:13:00.000-07:00

1) A 3 digit number is such that it's unit digit is equal to the product of the other two digits which are prime. Also, the difference between it's reverse and itself is 396.

What is the sum of the three digits?

2) Substitute numbers for the letters so that the following mathematical expressions are correct.

ABC DEF GHI

--- = IE --- = IE --- = IE

3 6 9

Note that the same number must be used for the same letter whenever it appears.

3) A, B, C and D are related to each other.

One of the four is the opposite sex from each of the other three.

D is A's brother or only daughter.

A or B is C's only son.

B or C is D's sister.

4) Dr. DoLittle always goes walking to the clinic and takes the same time while going and while coming back. One day he noticed something.

When he left the home, the hour hand and the minute hand were exactly opposite to each other and when he reached the clinic, they were together.

Similarly, when he left the clinic, the hour hand and the minute hand were together and when he reached the home, they were exactly opposite to each other.

How much time does Dr. DoLittle take to reach home from the clinic? Give the minimal possible answer.

5) SlowRun Express runs between Bangalore and Mumbai, For the up as well as the down journey, the train leaves the starting station at 10:00 PM everyday and reaches the destination at 11:30 PM after three days.

Mr. Haani once travelled by SlowRun Express from Mumbai to Bangalore. How many SlowRun Express did he cross during his journey?

6) Thus, Mr. Haani must have crossed 7 SlowRun Expresses during his journey.

Six cabins numbered 1-6 consecutively, are arranged in a row and are separated by thin dividers. These cabins must be assigned to six staff members based on following facts.

Miss Shalaka's work requires her to speak on the phone frequently throughout the day.

Miss Shudha prefers cabin number 5 as 5 is her lucky number.

Mr. Shaan and Mr. Sharma often talk to each other during their work and prefers to have adjacent cabins.

Mr. Sinha, Mr. Shaan and Mr. Solanki all smoke. Miss Shudha is allergic to smoke and must have non-smokers adjacent to her.

Mr. Solanki needs silence during work.

Can you tell the cabin numbers of each of them?

7) SkyFi city is served by 6 subway lines - A, E, I, O, U and Z.

When it snows, morning service on line E is delayed.

When it rains or snows, service on the lines A, U and Z is delayed both morning and afternoon.

When the temperature drops below 20 C, afternoon service is cancelled on either line A or line O, but not both.

When the temperature rises above 40 C, afternoon service is cancelled on either line I or line Z, but not both.

When service on line A is delayed or cancelled, service on line I is also delayed.

When service on line Z is delayed or cancelled, service on line E is also delayed.

On February 10, it snows all day with the temperature at 18C. On how many lines service will be delayed or cancelled, including both morning and afternoon?

SkyFi city is served by 6 subway lines - A, E, I, O, U and Z.

When it snows, morning service on line E is delayed.

When it rains or snows, service on the lines A, U and Z is delayed both morning and afternoon.

When the temperature drops below 20 C, afternoon service is cancelled on either line A or line O, but not both.

When the temperature rises above 40 C, afternoon service is cancelled on either line I or line Z, but not both.

When service on line A is delayed or cancelled, service on line I is also delayed.

When service on line Z is delayed or cancelled, service on line E is also delayed.

On February 10, it snows all day with the temperature at 18C. On how many lines service will be delayed or cancelled, including both morning and afternoon?

In a certain game, if 2 wixsomes are worth 3 changs, and 4 changs are worth 1 plut, then 6 plutes are worth how many wixsomes?

8) A 3 digit number is such that it's unit digit is equal to the product of the other two digits which are prime. Also, the difference between it's reverse and itself is 396.

What is the sum of the three digits?

9) There are 4 mugs placed upturned on the table. Each mug have the same number of marbles and a statement about the number of marbles in it. The statements are: Two or Three, One or Four, Three or One, One or Two.

Only one of the statement is correct. How many marbles are there under each mug?

10) At University of Probability, there are 375 freshmen, 293 sophomores, 187 juniors, & 126 seniors. One student will randomly be chosen to receive an award.

What percent chance is there that it will be a junior? Round to the nearest whole percent.

11) Assume for a moment that the earth is a perfectly uniform sphere of radius 6400 km. Suppose a thread equal to the length of the circumference of the earth was placed along the equator, and drawn to a tight fit.

Now suppose that the length of the thread is increased by 12 cm, and that it is pulled away uniformly in all directions.

By how many cm. will the thread be separated from the earth's surface?

12) Scientist decided to do a study on the population growth of rabbits. Inside a controlled environment, 1000 rabbits were placed.

Six months later, there were 1000Z rabbits. At the beginning of the 3rd year, there were roughly 2828Z rabbits, which was 4 times what the scientists placed in there at the beginning of the 1st year.

If Z is a positive variable, how many rabbits would be there at the beginning of the 11th year?

13) A man is stranded on a desert island. All he has to drink is a 20oz bottle of sprite.

To conserve his drink he decides that on the first day he will drink one oz and the refill the bottle back up with water. On the 2nd day he will drink 2oz and refill the bottle. On the 3rd day he will drink 3oz and so on...

By the time all the sprite is gone, how much water has he drunk?

14) You have four 9's and you may use any of the (+, -, /, *) as many times as you like. I want to see a mathematical expression which uses the four 9's to = 100

How many such expressions can you make?

15) In a certain year, the number of girls who graduated from City High School was twice the number of boys. If 3/4 of the girls and 5/6 of the boys went to college immediately after graduation, what fraction of the graduates that year went to college immediately after graduation?

16) A mule and a donkey were carrying full sacks on their backs.

The mule started complaining that his load was too heavy. The donkey said to him "Why are you complaining? If you gave me one of your sacks I'd have double what you have and if I give you one of my sacks we'd have an even amount."

How many sacks were each of them carrying? Give the minimal possible answer

17) Two people enter a race in whick you run to a point and back. Person A runs 20 mph to and from the point. Person B runs to the point going 10 mph and 30 mph going back.

Who came in first?

18) Three friends divided some bullets equally. After all of them shot 4 bullets the total number of bullets remaining is equal to the bullets each had after division. Find the original number divided.

19) Find sum of digits of D.
Let A= 1999 (power) 1999

B = sum of digits of A, C = sum of digits of B, D = sum of digits of C. (HINT: A = B = C = D (mod 9))

20) There is a 50m long army platoon marching ahead. The last person in the platoon wants to give a letter to the first person leading the platoon. So while the platoon is marching he runs ahead, reaches the first person and hands over the letter to him and without stopping he runs and comes back to his original position.In the mean time the whole platoon has moved ahead by 50m.The question is how much distance did the last person cover in that time. Assuming that he ran the whole distance with uniform speed.

21) If you take a marker & start from a corner on a cube, what is the maximum number of edges you can trace across if you never trace across the same edge twice, never remove the marker from the cube, & never trace anywhere on the cube, except for the corners & edges?

22) One of Mr. Bajaj, his wife, their son and Mr. Bajaj's mother is an Engineer and another is a Doctor.

If the Doctor is a male, then the Engineer is a male.

If the Engineer is younger than the Doctor, then the Engineer and the Doctor are not blood relatives.

If the Engineer is a female, then she and the Doctor are blood relatives.

Can you tell who is the Doctor and the Engineer?

23)Three men - Sam, Cam and Laurie - are married to Carrie, Billy and Tina, but not necessarily in the same order.
Sam's wife and Billy's Husband play Carrie and Tina's husband at bridge. No wife partners her husband and Cam does not play bridge.
Who is married to Cam?

24) There are 3 persons X, Y and Z. On some day, X lent tractors to Y and Z as many as they had. After a month Y gave as many tractors to X and Z as many as they have. After a month Z did the same thing. At the end of this transaction each one of them had 24.

Find the tractors each originally had?

25) A certain street has 1000 buildings. A sign-maker is contracted to number the houses from 1 to 1000. How many zeroes will he need?

26) There are 9 coins. Out of which one is odd one i.e weight is less or more. How many iterations of weighing are required to find odd coin?

27) In a sports contest there were m medals awarded on n successive days (n > 1).

On the first day 1 medal and 1/7 of the remaining m - 1 medals were awarded.

On the second day 2 medals and 1/7 of the now remaining medals was awarded; and so on.

On the nth and last day, the remaining n medals were awarded.

How many days did the contest last, and how many medals were awarded altogether?

28) A number of 9 digits has the following properties:

The number comprising the leftmost two digits is divisible by 2, that comprising the leftmost three digits is divisible by 3, the leftmost four by 4, the leftmost five by 5, and so on for the nine digits of the number i.e. the number formed from the first n digits is divisible by n, 2<=n<=9.

Each digit in the number is different i.e. no digits are repeated.

The digit 0 does not occur in the number i.e. it is comprised only of the digits 1-9 in some order.

Find the number.

Practice Puzzle 1

2007-05-29T22:11:00.000-07:00

1) How many ways are there of arranging the sixteen black or white pieces of a standard international chess set on the first two rows of the board?

Given that each pawn is identical and each rook, knight and bishop is identical to its pair.

2) A person with some money spends 1/3 for cloths, 1/5 of the remaining for food and 1/4 of the remaining for travel. He is left with Rs 100/-

How much did he have with him in the begining?

3) Grass in lawn grows equally thick and in a uniform rate. It takes 24 days for 70 cows and 60 days for 30 cows to eat the whole of the grass.

How many cows are needed to eat the grass in 96 days?

4) There is a safe with a 5 digit number as the key. The 4th digit is 4 greater than the second digit, while the 3rd digit is 3 less than the 2nd digit. The 1st digit is thrice the last digit. There are 3 pairs whose sum is 11.

Find the number.

5) Find the smallest number such that if its rightmost digit is placed at its left end, the new number so formed is precisely 50% larger than the original number.
Answer

6) Two identical pack of cards A and B are shuffled throughly. One card is picked from A and shuffled with B. The top card from pack A is turned up. If this is the Queen of Hearts, what are the chances that the top card in B will be the King of Hearts?

7) There is a 4-character code, with 2 of them being letters and the other 2 being numbers.

How many maximum attempts would be necessary to find the correct code? Note that the code is case-sensitive.

8)How many possible combinations are there in a 3x3x3 rubics cube?

In other words, if you wanted to solve the rubics cube by trying different combinations, how many might it take you (worst case senerio)?

How many for a 4x4x4 cube?

9)Substitute digits for the letters to make the following relation true.

N E V E R

L E A V E

+ M E

-----------

A L O N E

Note that the leftmost letter can't be zero in any word. Also, there must be a one-to-one mapping between digits and letters. e.g. if you substitute 3 for the letter M, no other letter can be 3 and all other M in the puzzle must be 3.

10)One of the four people - Mr. Clinton, his wife Monika, their son Mandy and their daughter Cindy - is a singer and another is a dancer. Mr. Clinton is older than his wife and Mady is older than his sister.

If the singer and the dancer are the same sex, then the dancer is older than the singer.

If neither the singer nor the dancer is the parent of the other, then the singer is older than the dancer.

If the singer is a man, then the singer and the dancer are the same age.

If the singer and the dancer are of opposite sex then the man is older than the woman.

If the dancer is a woman, then the dancer is older than the singer.

Whose occupation do you know? And what is his/her occupation?

11) In a hotel, rooms are numbered from 101 to 550. A room is chosen at random. What is the probability that room number starts with 1, 2 or 3 and ends with 4, 5 or 6?

12) There are 3 persons X, Y and Z. On some day, X lent tractors to Y and Z as many as they had. After a month Y gave as many tractors to X and Z as many as they have. After a month Z did the same thing. At the end of this transaction each one of them had 24.

Find the tractors each originally had?

13) You have 14 apples. Your Friend Marge takes away 3 and gives you 2. You drop 7 but pick up 4. Bret takes 4 and gives 5. You take one from Marge and give it to Bret in exchange for 3 more. You give those 3 to Marge and she gives you an apple and an orange. Frank comes and takes the apple Marge gave you and gives you a pear. You give the pear to Bret in exchange for an apple. Frank then takes an apple from Marge, gives it to Bret for an orange, gives you the orange for an apple.

How many pears do you have?

14) There were N stations on a railroad. After adding X stations 46 additional tickets have to be printed.

Find N and X.

15) An emergency vehicle travels 10 miles at a speed of 50 miles per hour.

How fast must the vehicle travel on the return trip if the round-trip travel time is to be 20 minutes?

16) All of the students at a college are majoring in psychology, business, or both. 73% of the students are psychology majors, & 62% are business majors.

If there are 200 students, how many of them are majoring in both psychology & business?

17) Karan bought a little box of midget matches, each one inch in length. He found that he could arrange them all in the form of a triangle whose area was just as many square inches as there were matches.

He then used up six of the matches, and found that with the remainder he could again construct another triangle whose area was just as many square inches as there were matches.

And using another six matches he could again do precisely the same.

How many matches were there in the box originally?

Note that the match-box can hold maximum of 50 matches.

18) Mr. Black, Mr. White and Mr. Grey were chatting in the Yahoo conference. They were wearing a black suit, a white suit and a grey suit, not necessarily in the same order.

Mr. Grey sent message, "We all are wearing suit that are of the same color as our names but none of us is wearing a suit that is the same color as his name."

On that a person wearing the white suit replied, "What difference does that make?"

Can you tell what color suit each of the three persons had on?

Puzzle 5

2007-05-29T21:47:00.001-07:00

Q.A survey was taken among 100 people to find their preference of watching T.V. programmes. There are 3 channels. Given the no of people who watch.

at least channel 1

at least channel 2

at least channel 3

no channels at all

atleast channels 1 and 3

atleast channels 1 and 2

atleast channels 2 and 3

Find the no of people who watched all three.

Q. Albert and Fernandes have two leg swimming race. Both start from opposite ends of the pool. On the first leg, the boys pass each other at 18 m from the deep end of the pool. During the second leg they pass at 10 m from the shallow end of the pool.

Both go at constant speed but one of them is faster.

Each boy rests for 4 seconds at the end of the first leg.

What is the length of the pool?

Q. Each alphabet stands for one digit in the following multiplication.

T H I S

x I S

---------

X F X X

X X U X

------------

X X N X X

------------

What is the maximum value T can take?

Ans: T max value = 4

Q.An escalator is descending at constant speed.

A walks down and takes 50 steps to reach the bottom.

B runs down and takes 90 steps in the same time as A takes 10 steps.

How many steps are visible when the escalator is not operating?

Ans: 150 steps

Q. Every day a cyclist meets a train at a particular crossing. The road is straight before the crossing and both are travelling in the same direction.The cyclist travels with a speed of 10 Kmph. One day the cyclist comes late by 25 min. and meets the train 5km before the crossing. What is the speed of the train?

Ans: 60 kmph

Q.There are five persons with surnames Mukherjee, Misra, Iyer, Patil and Sharma. There are 4 persons having first or middle name of Kumar, 3 persons with Mohan, 2 persons with Dev and 1 Anil. Either Mukherjee and Patil have a first or middle name of Dev or Misra and Iyer have their first or middle name of Dev Of Mukherkjee and Misra, either both of them have a first or middle name of Mohan or neither have a first or middle name of Mohan. Either Iyer or Sharma has a first or middle name of Kumar but not both. Who has the first or middle name of Anil?

Ans: Kumar Misra Dev

Mohan Iyer Dev

Kumar Patil Mohan

Mohan Sharma Kumar

Q. Boys are allowed to watch football at C.V.Raman auditorium subjected to conditions. The boy over age 16 can wear overcoat.No boy over age 15 can wear cap. To watch the football either he has to wear overcoat or cap or both A boy with an umberella or above 16 or both cannot wear sweater. Boys must either not watch football or wear sweater.

What is the appearence of the boy who is watching football.

Q. A bird keeper has got P pigeons, M mynas and S sparrows.The keeper goes for lunch leaving his assistant to watch the birds.Suppose p=10, m=5, s=8 when the bird keeper comes back, the assistant informs the x birds have escaped. The bird keeper claims: "Oh no! All my sparrows are gone." How many birds flew away?

When the bird keeper comes back, the assistant told him that x birds have escaped. The keeper realised that atleast 2 sparrows have escaped. What is minimum no of birds that can escape?

Q. Answer the following questions based on the conditions from the choices. A, B, C, D, E as described below:

(A) if a definete conclusion can be drawn from condition 1

(B) if a definete conclusion can be drawn from condition 2

(C) if a definete conclusion can be drawn from condition 1 and 2

(D) if a definete conclusion can be drawn from condition 1 or 2

(E) no conclusion can be drawn using both conditions

person 1 says N<5
Persons 2 says N > 5
person 3 says 3N>20
person 4 says 3N>10
person 5 says N<8

What is the value of N?

a)

1. No of persons who speak false being less than no of persons who tells the truth.

2. Person 2 is telling the truth.

b)

1. no of persong telling the truth is greater than no of persons telling lies

2. person 5 is telling the truth.

Q. There are N coins on a table and there are two players A & B. You can take 1 or 2 coins at a time. The person who takes the last coin is the loser. A always starts first.

If N=7

(a) A can always win by taking two coins in his first chanse

(b) B can win only if A takes two coins in his first chance.

(c) B can always win by proper play

(d) none of the above

2. A can win by proper play if N is equal to

(a) 13 (b) 37 (c) 22 (d) 34 (e) 48

Ans: (e.)

3. B can win by proper play if N is equal to

(a) 25 (b)26 (c) 32 (d) 41 (e) none

4. if N<4, can A win by proper play always?

(a) Yes (b) No

Q. Two twins have vertain peculiar charcteristics.

One of them always lies on Monday, Wednesday, Friday.

The other always lies on Tuesdays, Thursdays and Saturdays.

On the other days they tell the truth. You are given a conversation.

Person A-- today is Sunday my name is Anil

Person B -- today is Tuesday, my name is Bill

What day is today?

Ans: Today is Tuesday

Q. There is a safe with a 5 digit number as the key.

The 4th digit is 4 greater than second digit, while 3rd digit is 3

less than 2nd digit. The 1st digit is thrice the last digit.

There are 3 pairs whose sum is 11.

Find the number.

Ans: 65292

Q. A hotel has two wings,the east wing and the west wing.

Some east wing rooms but not all have an ocean view.

All west wing rooms have a harbour view.

The charge for all rooms is identical, except as follows :

Extra charge for all harbour view rooms on or above the 3rd floor

Extra charge for all ocean view rooms except those without balcony

Extra charge for some harbour rooms on the first two floor & some

east wing rooms without ocean view but having kitchen facilities.

Which of the following cannot be determined on the basis of the

nformation given:

I. Whether there are any rooms without a balcony for which an extra

charge is imposed.

II. Whether any room without a kitchen or a view involves an extra

charge.

III. Whether two extra charges are impsed for any room.

(A) I only

(B) II only

(C) III only

(D) II and III only

(E) I, II and III

Ans: (A)

Puzzle 4

2007-05-29T21:46:00.000-07:00

Q. Replace each letter by a digit. Each letter must be represented by the same digit and no beginning letter of a word can be 0.

O N E

O N E

O N E

O N E

-------

T E N

Ans: 0 =1, N = 8 ,E = 2, T = 7

Q.Ann, Boobie, Cathy and Dave are at their monthly business meeting. Their occupations are author, biologist, chemist and doctor, but not necessarily in that order.Dave just told the biologist that Cathy was on her way with doughnuts. Ann is sitting across from the doctor and next to the chemist.The doctor was thinking that Boobie was a goofy name for parent's to choose,but didn't say anything.What is each person's occupation?

Ans: Since Dave spoke to the biologist and Ann sat next to the chemist and across the doctor, Cathy must be the author and Ann the biologist.

The doctor didn't speak, but David did, so Bobbie is the doctor and Dave the chemist.

Q.Sometime after 10:00 PM a murder took place. A witness claimed that the clock must have stopped at the time of the shooting. It was later found that the postion of both the hands were the same but their positions had interchanged. Tell the time of the shooting (both actual and claimed).

Ans: Time of shooting = 11:54 PM

Claimed Time = 10:59 PM

Q. Next number in the series is 1 , 2 , 4 , 13 , 31 , 112 , ?

Ans: 224.

Sol. No number has digits more than 4. All of them are 1 , 2, 4, 8 , 16 ,32 , 64 converted to numbers in base 5

Q. Shahrukh speaks truth only in the morning and lies in the afternoon, where as Salman speaks truth only in the afternoon. A says that B is Shahrukh. Is it morning or afternoon and who is A -
Shahrukh or Salman.

Ans: Afternoon ; A is Salman.

Q.Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination 1 hr and 4 hours respectively after passing each other. How nuch faster is one train from other?

Ans: Twice

Q.There are 6 volumes of books on a rack kept in order ( ie vol.1, vol. 2 and so on ).

Give the position after the following changes were noticed.

All books have been changed

Vol.5 was directly to the right of Vol.2

Vol.4 has Vol.6 to its left and both weren't at Vol.3's place

Vol.1 has Vol.3 on right and Vol.5 on left

An even numbered volume is at Vol.5's place

Find the order in which the books are kept now.

Q. A chain is broken into three pieces of equal lenths containing 3 links each.It is taken to a backsmith to join into a single continuous one .How many links are to to be opened to make it ?

Ans : 2.

Q.Grass in lawn grows equally thick and in a uniform rate.It takes 24 days for 70 cows and 60 days for 30 cows to eat the whole of the grass.

How many cows are needed to eat the grass in 96 days.?

Ans : 20

Sol.

g - grass at the beginning

r - rate at which grass grows, per day

y - rate at which one cow eats grass, per day

n - no of cows to eat the grass in 96 days

g + 24*r = 70 * 24 * y

g + 60*r = 30 * 60 * y

g + 96*r = n * 96 * y

Solving, n = 20.

Q. From a vessel, 1/3rd of the liquid evaporates on the first day. On the second day 3/4th of the remaining liquid evaporates.What fraction of the volume is present at the end of the second day.

Ans: 50%

Q. An orange glass has orange juice and white glass has apple juice both of equal volumes.50ml of the orange juice is taken and poured into the apple juice.50ml from the white glass is poured into the orange glass. Of the two quantities, the amount of apple juice in the orange glass and the amount of orange juice in the white glass,which one is greater and by how much?

Ans: The two quantities are equal

Q.There is a 4 inch cube painted on all sides. This is cut down into of 1 inch cubes. What is the no of cubes which have no pointed sides.

Ans: 8

Q. Sam and Mala have a conversation. Sam says I am certainly not over 40.Mala says I am 38 and you are atleast 5 years older than me.Now Sam says you are atleast 39.

All the statements by the two are false.

How old are they really?

Ans: Mala = 38 yrs

Sam = 41 yrs.

Q. Ram Singh goes to his office in the city, every day from his suburban house. His driver Gangaram drops him at the railway station in the morning and picks him up in the evening. Every evening Ram Singh reaches the station at 5 O' Clock. Gangaram also reaches at the same time.One day Ram Singh started early from his office and came to the station at 4 O' Clock.Not wanting to wait for the car he starts walking home. Mangaram starts at normal time, picks him up on the way and takes him back house, half an hour early.How much time did Ram Singh walk?

Q. In a railway station, there are two trains going. One in the harbour line and one in the main line, each having a frequency of 10 minutes. The main line service starts at 5 o'clock and the harbour line starts at 5.02A.M. A man goes to the station every day to catch the first train that comes. What is the probability of the man catching the first train?

Ans: 0.8

Q.A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11 mornings and 12 afternoons. How many days did they stay there totally?

Ans: 18

Puzzle 3

2007-05-29T21:45:00.000-07:00

Q. Some statements are given below:

L says all of my other four friends have money

M says that P said that exactly one among them has money

N says that L said that precisely two among them have money

O says that M said that three of the others have money

P, L and N said that they have money

All the above statement are false. Who has money & who doesn't have any money?

Q. Mr.Mathurs jewels have been stolen from his bank locker .The bank has lockers of 12 people which are arranged in an array of 3 rows and 4 columns like:

1 2 3 4
5 6 7 8
9 10 11 12

The locker belonging to JONES was to the right of BLACK'S locker and directly above MILLAR'S.
BOOTH'S locker was directly above MILLAR'S.
SMITH'S locker was also above GRAY's (though not directly).
GREEN'S locker was directly below SMITH'S.
WILSON'S locker was between that of DAVIS and BOOTH.
MILLAR'S locker was on the bottom row directly to the right of HERD'S.
WHITE'S locker was on the bottom right hand corner in the same column as BOOTH'S.

Which box belonged to Mr.Mathurs?

Ans: Box number 9 belongs to Mr.Mathurs.

Q. Fifty minutes ago if it was four times as many minutes past three o'clock,how many minutes is it to six o'clock?

Ans: Twenty six minutes.

Q. If a clock takes 7seconds to strike 7, how long will the same clock take to strike 10?

sol: The clock strikes for the first time at the start and takes 7 seconds for 6 intervals-thus for one interval time taken=7/6.
Therefore, for 10 seconds there are 9 intervals and time taken is 9*7/6=10 and 1/2 seconds.

Q.Three criminals were arrested for shop lifting. However, when interrogated only one told the truth in both his statements, while the other two each told one true statement and one lie.

The statements were:

ALBERT :(a)Chander passed the merchandise.(b)Bruce created the diversion.

BRUCE :(a)Albert passed the merchandise. (b)I created the diversion.

CLIVE :(a)I took the goods out of the shop. (b)Bruce passed Them over.

Ans: Albert passed the goods.Bruce created the diversion..Clive took the goods out of the shop.

Q. I bought a car with a peculiar 5 digit numbered licence plate which on reversing could still be read. On reversing value is increased by 78633.Whats the original number if all digits were different?

Ans: Only 0 1 6 8 and 9 can be readupside down.So on rearranging these digits we get the answer as 10968

Q. The shape in the sketch below is that of a square attached to half of a similar square.Divide it into four equal pieces

Ans: Hint : the figure can be divided into 12 equal triangles

Q. Supposing a clock takes 7 seconds to strike 7. How mlong will it take to strike 10?

Ans: 10 1/2 seconds.

Q. A man collects cigarette stubs and makes one full cigarette with every 8 stubs.If he gets 64 stubs how many full cigarettes can he smoke.

Ans: 8+1=9

Q. A soldier looses his way in a thick jungle. At random he walks from his camp but mathematically in an interesting fashion.First he walks one mile East then half mile to North. Then 1/4 mile to West, then 1/8 mile to South and so on making a loop.Finally how far he is from his camp and in which direction.

Ans: Distance travelled in north and south directions

1/2 - 1/8 + 1/32 - 1/128 + 1/512 - and so on = 1/2/((1-(-1/4))

Similarly in east and west directions

1- 1/4 + 1/16 - 1/64 + 1/256 - and so on = 1/(( 1- ( - 1/4))

Add both the answers

Q.How can 1000000000 be written as a product of two factors neither of them containing zeros

Ans: 2 power 9 x 5 power 9

Q. Conversation between two mathematcians:

First : I have three childern. The product of their ages is 36. If you sum their ages, it is exactly same as my neighbour's door number on my left.The second mathematician verfies the door number and says that it is not sufficient.Then the first says " Ok one more clue is that my youngest is really the youngest". Immmediately the second mathematician answers .Can you answer the question asked by the first mathematician? What are the childeren ages?

Ans: 1,6 and 6

Q.Light glows for every 13 seconds . How many times did it glow between 1:57:58 and 3:20:47 am.

Ans : 383 + 1 = 384

Q. 500 men are arranged in an array of 10 rows and 50 columns according to their heights. Tallest among each row of all are asked to fall out.And the shortest among them is A.Similarly after resuming that to their original podsitions that the shortest among each column are asked to fall out.

And the tallest among them is B .

Now who is taller among A and B ?

Ans : A

Q. A person with some money spends1/3 for cloths, 1/5 of the remaining for food and 1/4 of the remaining for travel.He is left with Rs 100/- .

How much did he have with him in the begining ?

Ans: Rs 250/-

Q. There are six boxes containing 5 , 7 , 14 , 16 , 18 , 29 balls of either red or blue in colour. Some boxes contain only red balls and others contain only blue.One sales man sold one box out of them and then he says " I have the same number of red balls left out as that of blue ".Which box is the one he solds out ?

Ans: Total no of balls = 89 and (89-29 /2) = 60/2 = 30 and also 14 + 16 = 5 + 7 + 18 = 30

Puzzle 2

2007-05-29T21:44:00.000-07:00

Q. At 6'o a clock ticks 6 times. The time between first and last ticks is 30 seconds. How long does it tick at 12'o clock.

Ans: 66 sec.

Q. Three friends divided some bullets equally. After all of them shot 4 bullets the total number of bullets remaining is equal to the bullets each had after division. Find the original number divided.

Ans: 18

sol. Initially x x x

Now x-4 x-4 x-4

Equation is 3x-12 = x

Q. A ship went on a voyage. After it had travelled 180 miles a plane statrted with 10 times the speed of the ship. Find the distance when they meet from starting point.

Ans: 200miles.

Sol. Distance travelled by plane = 1/10 distance travelled by ship + 180.

Q. 3 societies A, B, C. A lent cars to B and C as many as they had already. After some time B gave as many tractors to A and C as many as they have. After sometime c did the same thing. At the end of this transaction each one of them had 24.Find the cars each orginally had.

Ans: A had 39 cars, B had 21 cars & C had 12 cars

Q. There N stations on a railroad.After adding X stations on the rail route 46 additional tickets have to be printed.Find N and X.

Ans. x=2 and N=11

Sol. Let initially, N(N-1) = t

After adding, (N+X)(N+X-1) = t+46

Q.Given that April 1 is tuesday. A, B, C are 3 persons told that their farewell party was on

A - May 8, thursday

B - May 10,tuesday

C - June 5, friday

Out of A, B, C only one made a completetly true statement concerning date,day and month. The other told two one told the day right and the other the date right.. What is correct date, month, day.

Ans: B - (May 10) SUNDAY

C - June 6 (Friday).

Q. The Bulls, Pacers, Lakers and Jazz ran for a contest. Anup, Sujit, John made the following statements regarding results. Anup said either Bulls or Jazz will definitely win Sujit said he is confident that Bulls will not win John said he is confident that neither Jazz nor Lakers will win When the result cameit was found that only one of the above three had made a correct statement.

Who has made the correct statement and who has won the contest.

Ans: Sujith; Lakers

Q. Five people A ,B ,C ,D ,E are related to each other.

Four of them make one true statement each as follows.

(i) B is my father's brother.

(ii) E is my mother-in-law.

(iii)C is my son-in-law's brother

(iv)A is my brother's wife.

Ans:
(i) D

(ii) B

(iii) E

(iv) C

Q. Some statements are given below:

L says all of my other four friends have money

M says that P said that exactly one among them has money

N says that L said that precisely two among them have money

O says that M said that three of the others have money

P, L and N said that they have money

All the above statement are false. Who has money & who doesn't have any money?

Q. Mr.Mathurs jewels have been stolen from his bank locker .The bank has lockers of 12 people which are arranged in an array of 3 rows and 4 columns like:

1 2 3 4
5 6 7 8
9 10 11 12

The locker belonging to JONES was to the right of BLACK'S locker and directly above MILLAR'S.
BOOTH'S locker was directly above MILLAR'S.
SMITH'S locker was also above GRAY's (though not directly).
GREEN'S locker was directly below SMITH'S.
WILSON'S locker was between that of DAVIS and BOOTH.
MILLAR'S locker was on the bottom row directly to the right of HERD'S.
WHITE'S locker was on the bottom right hand corner in the same column as BOOTH'S.

Which box belonged to Mr.Mathurs?

Ans: Box number 9 belongs to Mr.Mathurs.

Q. Fifty minutes ago if it was four times as many minutes past three o'clock,how many minutes is it to six o'clock?

Ans: Twenty six minutes.

Q. If a clock takes 7seconds to strike 7, how long will the same clock take to strike 10?

sol: The clock strikes for the first time at the start and takes 7 seconds for 6 intervals-thus for one interval time taken=7/6.
Therefore, for 10 seconds there are 9 intervals and time taken is 9*7/6=10 and 1/2 seconds.

Q.Three criminals were arrested for shop lifting. However, when interrogated only one told the truth in both his statements, while the other two each told one true statement and one lie.

The statements were:

ALBERT :(a)Chander passed the merchandise.(b)Bruce created the diversion.

BRUCE :(a)Albert passed the merchandise. (b)I created the diversion.

CLIVE :(a)I took the goods out of the shop. (b)Bruce passed Them over.

Ans: Albert passed the goods.Bruce created the diversion..Clive took the goods out of the shop.

Puzzle 1

2007-05-29T21:43:00.000-07:00

Q. Father's age is three years more than three times the son's age.After three years, father's age will be ten years more than twice the son's age. What is the father's present age.

Ans: 33 years.

Q.Find the values of each of the alphabets.

N O O N

S O O N

+ M O O N

----------

J U N E

Ans: 9326

Q.There are 20 poles with a constant distance between each pole.A car takes 24 seconds to reach the 12th pole.

How much will it take to reach the last pole.

Ans: 41.45 seconds

Let the distance between two poles = x

Hence 11x:24::19x:?

Q.A car is travelling at a uniform speed.The driver sees a milestone showing a 2-digit number.After travelling for an hour the driver sees another milestone with the same digits in reverse order.After another hour the driver sees another milestone containing the same two digits.What is the average speed of the driver.

Ans: 45 kmph

Q.The minute and the hour hand of a watch meet every 65 minutes.How much does the watch lose or gain time and by how much?

Ans: Gains; 5/11 minutes

Q.Ram, Shyam and Gumnaam are friends. Ram is a widower and lives alone and his sister takes care of him. Shyam is a bachelor and his neice cooks his food and looks after his house. Gumnaam is married to Gita and lives in large house in the same town. Gita gives the idea that all of them could stay together in the house and share monthly expenses qually. During their first month of living together, each person contributed Rs.25. At the end of the month, it was found that Rs 92 was the expense so the remaining amount was distributed equally among everyone.The distribution was such that everyone recieved a whole number of Rupees.

How much did each person recieve?

Ans. Rs 2

(Hint: Ram's sister, Shyam's neice and Gumnaam's wife are the same person)

Q.Four persons A, B, C and D are playing cards.Each person has one card, laid down on the table below him, which has two different colours on either side. The colours visible on the table are Red, Green, Red and Blue. They see the color on the reverse side and give the following comment.

A: Yellow or Green
B: Neither Blue nor Green
C: Blue or Yellow
D: Blue or Yellow

Given that out of the 4 people 2 always lie find out the colours on the cards each person.

Puzzle Questions

2007-05-27T21:14:00.000-07:00

Puzzles:

Puzzle 1: Classic: If a bear walks one mile south, turns left and walks one mile to the east and then turns left again and walks one mile north and arrives at its original position, what is the color of the bear.
Puzzle 2: Given a rectangular (cuboidal for the puritans) cake with a rectangular piece removed (any size or orientation), how would you cut the remainder of the cake into two equal halves with one straight cut of a knife?
Puzzles 3: There are 3 baskets. one of them have apples, one has oranges only and the other has mixture of apples and oranges. The labels on their baskets always lie. (i.e. if the label says oranges, you are sure that it doesn't have oranges only,it could be a mixture) The task is to pick one basket and pick only one fruit from it and then correctly label all the three baskets.
Puzzles 4: You have 8 balls. One of them is defective and weighs less than others. You have a balance to measure balls against each other. In 2 weighings how do you find the defective one?
Puzzles 5: Why is a manhole cover round?
Puzzles 6: How many cars are there in the USA?
Puzzles 7: You've got someone working for you for seven days and a gold bar to pay them. The gold bar is segmented into seven connected pieces. You must give them a piece of gold at the end of every day. If you are only allowed to make two breaks in the gold bar, how do you pay your worker?
Puzzles 8: One train leaves Los Angeles at 15mph heading for New York. Another train leaves from New York at 20mph heading for Los Angeles on the same track. If a bird, flying at 25mph, leaves from Los Angeles at the same time as the train and flies back and forth between the two trains until they collide, how far will the bird have traveled?
Puzzles 9: You have two jars, 50 red marbles and 50 blue marbles. A jar will be picked at random, and then a marble will be picked from the jar. Placing all of the marbles in the jars, how can you maximize the chances of a red marble being picked? What are the exact odds of getting a red marble using your scheme?
Puzzles 10: Imagine you are standing in front of a mirror, facing it. Raise your left hand. Raise your right hand. Look at your reflection. When you raise your left hand your reflection raises what appears to be his right hand. But when you tilt your head up, your reflection does too, and does not appear to tilt his/her head down. Why is it that the mirror appears to reverse left and right, but not up and down?
Puzzles 11: You have 5 jars of pills. Each pill weighs 10 gram, except for contaminated pills contained in one jar, where each pill weighs 9 gm. Given a scale, how could you tell which jar had the contaminated pills in just one measurement?
Puzzles 12: If you had an infinite supply of water and a 5 quart and 3 quart pail, how would you measure exactly 4 quarts?
Puzzles 13: You have a bucket of jelly beans. Some are red, some are blue, and some green. With your eyes closed, pick out 2 of a like color. How many do you have to grab to be sure you have 2 of the same?
Puzzles 14: There are four dogs/ants/people at four corners of a square of unit distance. At the same instant all of them start running with unit speed towards the person on their clockwise direction and will always run towards that target. How long does it take for them to meet and where?
Puzzles 15: You're given an array containing both positive and negative integers and required to find the sub-array with the largest sum (O(N) a la KBL). Write a routine in C for the above.
Puzzles 16: Given an array of size N in which every number is between 1 and N, determine if there are any duplicates in it. You are allowed to destroy the array if you like. [ I ended up giving about 4 or 5 different solutions for this, each supposedly better than the others ].
Puzzles 17: Write a routine to draw a circle (x ** 2 + y ** 2 = r ** 2) without making use of any floating point computations at all. [ This one had me stuck for quite some time and I first gave a solution that did have floating point computations ].
Puzzles 18: Among 12 identical looking golf balls there is one that is defective in weight. It is either heavier or lighter than the standard one. You have a balance. You can only weigh 3 times to find out which one is defective and whether it is heavier or lighter.
Puzzles 19: There are 3 glasses. The biggest one can hold 24 ounces. The medium one can hold 11 ounces and the smallest one can hold 5 ounces. Now you have 24 ounces of soft drink in the largest glass. Can you use just these 3 glasses to make the largest glass contain 12 ounces of soft drink by pouring soft drink from one glass to another?
Puzzles 20: Eight eggs look identical except one is lighter. How can you weigh only 2 times on a balance scale to find out which one is lighter?