There are 3 pairs whose sum is 11. Find the number. Today's Puzzle Question

Tuesday, July 12, 2011

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.

Answer

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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?

Saturday, July 09, 2011

Question:

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?

Answer

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.

Todays Puzzle: How much did he have with him in the begining?

Friday, July 08, 2011

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?

Answer

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

Dear god

Tuesday, June 14, 2011

The love that u gave ,help my life to save,
You till color in my soul,give strength to reach my goal.
I am nothing without you, but there is a year too,
If you are not with me to upstay ,how can I spent my nioghT & day.
If you want my love to test,I am ready to show my best.
After this if I make this test clear ,please tell words of my love dear.
I am thankful of your,as this is only my life envisson.
I am not a poet to write a ryme,but I know you are mine Love makes the persons blind,change the life and change the mind

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?

Monday, March 21, 2011

Question:

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.

Answer

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

Today's Puzzle - How many earrings does Raj have?

Thursday, March 17, 2011

Question:

Raj has a jewel chest containing Rings, Pins and Ear-rings. The chest contains

26 pieces. Raj has 2 1/2 times as many rings as pins, and the number of pairs of

earrings is 4 less than the number of rings.

How many earrings does Raj have?

Answer:

12 earrings

Assume that there are R rings, P pins and E pair of ear-rings.

It is given that, he has 2 1/2 times as many rings as pins.

R = (5/2) * P or P = (2*R)/5

And, the number of pairs of earrings is 4 less than the number of rings.

E = R - 4 or R = E + 4

Also, there are total 26 pieces.

R + P + 2*E = 26

R + (2*R)/5 + 2*E = 26

5*R + 2*R + 10*E = 130

7*R + 10*E = 130

7*(E + 4) + 10*E = 130

7*E + 28 + 10*E = 130

17*E = 102

E = 6

Hence, there are 6 pairs of Ear-rings i.e. total 12 Ear-rings

Today's Puzzle - Finally how far he is from his camp and in which direction?

Wednesday, March 16, 2011

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?

Answer

The soldier is 0.8944 miles away from his camp towards East-North.

It is obvious that he is in East-North direction.

Distance travelled in North and South directions

= 1/2 - 1/8 + 1/32 - 1/128 + 1/512 - 1/2048 + and so on... (a geometric series with

r = (-1/4) )

(1/2) * ( 1 - (-1/4)n )

= ---------------------------

( 1 - (-1/4) )

= 1 / ( 2 * ( 1 - (-1/4) ) )

= 2/5

Similarly in East and West directions

= 1 - 1/4 + 1/16 - 1/64 + 1/256 - and so on... (a geometric series with r = (-1/4) )

(1) * ( 1 - (-1/4)n )

= ---------------------------

( 1 - (-1/4) )

= 1 / ( ( 1- (-1/4) )

= 4/5

So the soldier is 4/5 miles away towards East and 2/5 miles away towards North.

So using right angled triangle, soldier is 0.8944 miles away from his camp.

Today's Puzzle At what time after 4.00 p.m. is the minutes hand of a clock exactly aligned with the hour hand?

Thursday, March 10, 2011

At what time after 4.00 p.m. is the minutes hand of a clock exactly aligned with

the hour hand?

Answer

4:21:49.5

Assume that X minutes after 4.00 PM minute hand exactly aligns with and hour

hand.

For every minute, minute hand travels 6 degrees.

Hence, for X minutes it will travel 6 * X degrees.

For every minute, hour hand travels 1/2 degrees.

Hence, for X minutes it will travel X/2 degrees.

At 4.00 PM, the angle between minute hand and hour hand is 120 degrees. Also,

after X minutes, minute hand and hour hand are exactly aligned. So the angle

with respect to 12 i.e. Vertical Plane will be same. Therefore,

6 * X = 120 + X/2

12 * X = 240 + X

11 * X = 240

X = 21.8182

X = 21 minutes 49.5 seconds

Hence, at 4:21:49.5 minute hand is exactly aligned with the hour hand.

Today's Puzzle Substitute digits for the letters to make the following Division true

Tuesday, March 08, 2011

Question:

Substitute digits for the letters to make the following Division true

O U T

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

S T E M | D E M I S E

| D M O C

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

T U I S

S T E M

----------

Z Z Z E

Z U M M

--------

I S T

Note that the leftmost letter can't be zero in any word. Also, there must be a oneto-

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

Answer

C=0, U=1, S=2, T=3, O=4, M=5, I=6, Z=7, E=8, D=9

It is obvious that U=1 (as U*STEM=STEM) and C=0 (as I-C=I).

S*O is a single digit and also S*T is a single digit. Hence, their values (O, S, T)

must be 2, 3 or 4 (as they can not be 0 or 1 or greater than 4).

Consider, STEM*O=DMOC, where C=0. It means that M must be 5. Now, its

simple. O=4, S=2, T=3, E=8, Z=7, I=6 and D=9.

O U T 4 1 3

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

S T E M | D E M I S E 2 3 8 5 | 9 8 5 6 2 8

| D M O C | 9 5 4 0

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

T U I S 3 1 6 2

S T E M 2 3 8 5

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

Z Z Z E 7 7 7 8

Z U M M 7 1 5 5

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

I S T 6 2 3

Also, when arranged from 0 to 9, it spells CUSTOMIZED.

Today's Puzzle How much should the individual student pay for their journey?

Thursday, March 03, 2011

Question:

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?

Answer:

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.