Puzzles Contest - 7 With Answers

[HELP]

1. For doing the interior decorations of my apartment, < ="text/"> I have bought a roll of roofing paper. I do not know its exact thitkness, but let us assume it is X. How can I find out how long the roll is without unrolling it? In other words, can you derive a formula for length of roll if the radius is r?


2. The numbers 220 and 284 are known as amicable numbers. The reason is the sum of the proper divisions of220 equals 284 and what is even more interesting is the sum of the proper divisors of 284 equals 220. $0 far about 100 pairs of amicable numbers are known. Can you find some in four digits?


3. Vikram Chadda has two children, and at least one of them is a girl. What is the probability that both children. are girls?

4. In India water lillies grow extremely rapidly in the ponds. If the growth enlarged so much that each day it covered a surface double that which it filled the day before, so that at the end of the 20th day if entirely covered the pond, in which it grew, how long would it take two water lillies Qf the same size at the outset and at the same rate of growth to cover the same pond?


5.You were to count one number per second and counted seven hours per day, how long would it tcike you to count to a Billion?

6. Every man or woman alive today had 2 parents, 4 grand-parents, 8 great-grand parents, 16 great-great- grand parents, 32 great, great, great grand parents and so on. Let us take the case of Ram. Two generations ago Ram had 2 x 2 or22, or 4 ancestors. Three generations ago he had 2 x 2 x 2 or 23 or 8 ancestors. Four generations ago he had 2 x 2 x 2 x2 or 24 or 16 ancestors.
Assuming that there are 20 years to a generation, can you tell 400 years back how many ancestors did Ram have?

7.A cylindrical container has a radius of eight inches and a height of three inches. Compute how any inches should be added to either the radius or height to give the same increase in
the volume?

8 re is a piece of Mnemonic: . Now I - even I, would celebrate In rhymes unapt the great Immortal syracusan rivaled never more, who in his wondrous lore Passed on befare,Left men his guidance How to circles mensurate


9. It was a long drive. I drove 60 kilometres at 30 kilometres per hour and then an additional 60 kilo metres at 50 kilometres per hour.Compute my average speed over 120 kms


10.1, 2, 3, 4, 5, 6, 7, 8, 9 Here are the nine digits. Can you arrange the nine digits in order from left to right and + or - signs only so as to produce a result of 100?

Answers

1. The area of the edge of the paper which is a rectangle equals the area of the end of
the roll. If the radius of the roll is R, then R2 = WI or 1 =R2/W


2. 1184 - 6368,
2620 - 5564,
5020 - 2924,
6232 – 1210


3.There are three possible outcomes: G - B, B - G or G - G. Since only one of these three is girls the probability is 1/3


4. 19 days


5. About 109 years


6.1048576 - 400 years ago, that is 20 generations back, Ram - for that matter each one of
us had 220 or 1048576 ancestors supposing the change in radius or height be Then (8)2 (3 + x) = (8 + X)2 (3) X = 16/3


7. ;supposing the change in radius or height be Then (8)2 (3 + x) = (8 + X)2 (3)
X = 16/3


8. Pi to 30decimal places

9. Time required for the first sixty miles : 120 minutes Time required for the second sixty miles: 72 minutes Total time required : 192 minutes I travelled 120 miles in 192 minutes. Therefore the
average speed in miles per hour was: 60 x 120 = 371/2
- 192

10. 123 - 45 - 67 + 89
Also 1 +2+3+4+5+6+7+8 x9
Edited by: HELP

[keerthi]

3. Vikram Chadda has two children, and at least one of them is a girl. What is the probability that both children. are girls?
Ans) Probability = 1/2
Sol: there are only two possible ways becoz given atleast one is a girl
1) boths are girls
2) one girl and one boy
So prob of both girls = 1/2Edited by: keerthi

[keerthi]

4. In India water lillies grow extremely rapidly in the ponds. If the growth enlarged so much that each day it covered a surface double that which it filled the day before, so that at the end of the 20th day if entirely covered the pond, in which it grew, how long would it take two water lillies Qf the same size at the outset and at the same rate of growth to cover the same pond?

Ans)19 days
One water lilly can cover the whole pond in 20 days. And the pond is half filled in the 19th day.
So if there are two such water lilies the pond can be covered in 19 days.Edited by: keerthi

[keerthi]

9. It was a long drive. I drove 60 kilometres at 30 kilometres per hour and then an additional 60 kilo metres at 50 kilometres per hour.Compute my average speed over 120 kms



Ans)37.5 kmph


time for first 60 kms = 60/30 = 2hrs


time for second 60 kms = 60/50 =1.2hrs


Average speed = total distance/ total time = 120/3.2= 37.5 KmphEdited by: keerthi

[keerthi]

7.A cylindrical container has a radius of eight inches and a height of three inches. Compute how any inches should be added to either the radius or height to give the same increase in the volume?

Let the quantity to be incremented for radiusor height be ='x'
Volume must be same in both the cases
volume of cylinder = pi *r*r*h
pi*(8+x)(8+x)(3) = pi*(8)(8) (3+x)
solving we get x=16/3

[lenin]

[keerthi]

5.You were to count one number per second and counted seven hours per day, how long would it tcike you to count to a Billion?



Ans)


Per day 7 hours means it equals =7*60*60 =25200 numbers


One billion=10 power 9


billion no can be counted in =10power 9/25200 = 39682.5 days = 109 years

[keerthi]

6. Every man or woman alive today had 2 parents, 4 grand-parents, 8 great-grand parents, 16 great-great- grand parents, 32 great, great, great grand parents and so on. Let us take the case of Ram. Two generations ago Ram had 2 x 2 or22, or 4 ancestors. Three generations ago he had 2 x 2 x 2 or 23 or 8 ancestors. Four generations ago he had 2 x 2 x 2 x2 or 24 or 16 ancestors.
Assuming that there are 20 years to a generation, can you tell 400 years back how many ancestors did Ram have?
Ans)
400 years means 20 genrations
2generations back he has 2power2 ancesters
3 generations back he has 2power3 ancesters
20 generations back he has 2power20 ancestors = 10,48,576 ancestors

[keerthi]

10.1, 2, 3, 4, 5, 6, 7, 8, 9 Here are the nine digits. Can you arrange the nine digits in order from left to right and + or - signs only so as to produce a result of 100?
Ans) 123+45-67+8-9

[meenakshisekar]

7.A cylindrical container has a radius of eight inches and a height of three inches. Compute how any inches should be added to either the radius or height to give the same increase in
the volume?

let the inches be x
vol of cylinder=pi*r*r*h
22/7*(x+8)*(x+8)*3=22/7*8*(x+3)
ans:16/3

[rathour]

6. Every man or woman alive today had 2 parents, 4 grand-parents, 8 great-grand parents, 16 great-great- grand parents, 32 great, great, great grand parents and so on. Let us take the case of Ram. Two generations ago Ram had 2 x 2 or22, or 4 ancestors. Three generations ago he had 2 x 2 x 2 or 23 or 8 ancestors. Four generations ago he had 2 x 2 x 2 x2 or 24 or 16 ancestors.
Assuming that there are 20 years to a generation, can you tell 400 years back how many ancestors did Ram have?
ans:-
from the last para its clear that 400 years back & 20 yrs of generation it means 20 ancestors
so,for2 gene back :-2power 2 ans so on....................
similarly 20gene back:2 power 20 ans

[meera]

.10)1, 2, 3, 4, 5, 6, 7, 8, 9 Here are the nine digits. Can you arrange the nine digits in order from left to right and + or - signs only so as to produce a result of 100?


123+45-67+8-9

[meera]

3. Vikram Chadda has two children, and at least one of them is a girl. What is the probability that both children. are girls?
prob=1/2