Puzzles Contest -8 With Answers

[HELP]

1. The sum ot two numbers is ten. Their product is twenty. Can you find the sum of the reciprocals of the two numbers?



2. Is it possible that there are 53 Tuesdays in a non-leap year? What is the probability?


3.A friend of mme asked me to write down any multidigit number. But, he put a condition, the number should not end with a zero.I put down the number 96452Then he asked me to add up the five digits and subtract the total from the original number. I did and here is what I got: 96452 - 26 = 96426
He then asked me to cross out anyone of the five digits and tell him the remaining numbers. I crossed out the 2 and told him the rest of the digits. I neither told him the original number nor what I had done with it. Yet 'pop' he told me the exact number I had crossed out.
How do you explain it?


4. It was Mammu's birthday and I decided to buy for her some sweets. There was an old woman in the candy shop. I noticed something very strange, while she was weighing out the sweets. She had just six wieghts and a balance scale. That's all she had. With just this she was able to weigh any unit number of ounces of candy-right from 1 to 364.
Can you say what the six weights were?


5. Here is an epitaph of the celebrated Greek mathematician of 250 A.D., Diophantus. Can you calculate- his age from this? DlOPHANTUS PASSED ONE SIXTH OF HIS LIFE IN CHILDHOOD, ONE TWELFTH IN YOUTH, AND ONE SEVENTH MORE AS A BACHELOR; FIVE YEARS AFTER HIS MARRIAGE A SON WAS BORN WHO DIED FOUR YEARS BEFORE HIS FATHER AT HALF HIS FINAL AGE.
HOW OLD IS DIOPHANTUS?

6.What will be the h~ight of a pole made up of all the millimetre cubes in one cubic metre, if placed one on top of another.?

7.Co'nvert into Roman Figures Can you write 1789 in Roman figures?

8 Find out the Time What does 1408 hours mean?

9.A Problem of Thickness We have a large, very thin sheet of rice paper which pile at the rate. of one thousand sheels to the inch Supposing we tear the paper in half and put the two pieces together, on top of each other, and we tear them in half and put the four pieces together in a pile and then we tear them again in half and put the eight pieces together in a pile, and we continue like this upto fifty times, can you tell how high the final stack of paper would be?

10.Find out the Pattern What do you think the following pattern is? 6, 24, 60, 120, 210, 336

Answers

1. This problem can be worked by simul-. taneous equations, but the solution shown
below is a more clever, more intuitive approach

2. n7. 52 x 7 = 364 364 + 1 = 365 days Urhere are 52 of each day plus 1 extra day. Thus
the probability of anyone day -of week occurring, in a non-leap Year is one-seventh.
3. Very simple. .All you have to do is to find the digit which, added to the two you will
get nearest divisible by 9. For example, in 639, I crossed out the 3, and I told him the othEV two 6 and 9. All he had to do was add them and get 15. The nearest number divisible by 9 is 18. Therefore the missing number is 3.
4. 1,3, 9, 27, 81, 243. All powers of three

5. "Let us assume a is 'Diophantus' age a/6 + a/12 + a/7 + 5 + aj2 + 4 = a; a = 84 Diaphantus lived to be 84 years old
6.You will be stunned at the answer. The pole would be 1000 kilo metres high. Let us try to cal
culate it mentally.A cubic metre equals: 1000 cubic millimetre x 1000 x 1000.
One thousand millimetre cubes placed one atop another will make a pole 1 metre in height. And since we have 1000 x 1000 times more cubes, we shall have a - pole that is 1000 kilometres long
7.MDCCLXXXIX
8.1t 1408 hours is actually 8 minutes past 2 P.M."I'rhis is the system of twenty-four-hour clock.
Writing the hours and minutes this way is a sensible means of avoiding any confusion between A.M. and P.M.This system which is commonly used in the railway time tqbles in continent of Europe leave no possible doubt about the time of the day or night when a train is due to leave a station. Midnight is expressed as 0000 hours.
9. " £:The first tear results in two, or 21, pieces of paper. The second tear results in four or 22 pieces, the third tear eight or 23, the fourth in sixteen or24 pieces and so on. It is evident at once that after the fiftieth tear the stack will consist of 250 sheets of paper which equals - 11258 9990 6842 624 Now, we know that there are a thousand sheets to the inch. Therefore the stack will be about 1125899906842 inches high.To get the height of the stack in feet we have todivide this number by 12 and to get it in miles we have to divide the resulting number by 5280. The final result will be well over 17,000,000 miles

10. 6.7. 8.,
7.8.9.
8.9.10

Edited by: HELP

[meenakshisekar]

10.Find out the Pattern What do you think the following pattern is? 6, 24, 60, 120, 210, 336



ans:1*6,6*4,4*30,30*7,7*48

[meenakshisekar]

6.What will be the h~ight of a pole made up of all the millimetre cubes in one cubic metre, if placed one on top of another


ans:


1000mm or 1 metre

[keerthi]

1. The sum ot two numbers is ten. Their product is twenty. Can you find the sum of the reciprocals of the two numbers?

Ans)1/2
x+y/xy = 10/20 = 1/2

[keerthi]

2. Is it possible that there are 53 Tuesdays in a non-leap year? What is the probability?
Probabilty = 1/7
In a non leap year we have 365 days and
exactly 52 weeks +1 day
this one can be any one of seven days
so probability =1/7

[keerthi]

6.What will be the h~ight of a pole made up of all the millimetre cubes in one cubic metre, if placed one on top of another.?


Ans) 10power6 metres


one cubic meter has = 10power9 millimeter cubes.


so height of pole = 10power9 millimeters = 10power6 meters

[keerthi]

8 )Find out the Time What does 1408 hours mean?
Ans)8 min past 2 PM

[keerthi]

10.Find out the Pattern What do you think the following pattern is? 6, 24, 60, 120, 210, 336
Ans) 1*2*3 ,2*3*4 , 3*4*5 , 4*5*6 , 5*6*7 , 6*7*8

[keerthi]

5. Here is an epitaph of the celebrated Greek mathematician of 250 A.D., Diophantus. Can you calculate- his age from this? DlOPHANTUS PASSED ONE SIXTH OF HIS LIFE IN CHILDHOOD, ONE TWELFTH IN YOUTH, AND ONE SEVENTH MORE AS A BACHELOR; FIVE YEARS AFTER HIS MARRIAGE A SON WAS BORN WHO DIED FOUR YEARS BEFORE HIS FATHER AT HALF HIS FINAL AGE.
HOW OLD IS DIOPHANTUS?
Ans)84
the son died 4 years before the present age of father
And at that time his age was half his fathers present age .
So let fathers age be 'x'
then x = [1/6(x) + 1/12(x) + 1/7(x) + 5 + x/2 ]+ 4
solving we get x=84

[Dr YVS]

3) Sum of all numbers, shall be nine, hence easy to answer.

[meera]

1. The sum ot two numbers is ten. Their product is twenty. Can you find the sum of the reciprocals of the two numbers?

soln:
let x,y be 2 nos
x+y=10
x*y=20
sum of reciprocal=1/x+1/y
=y+x/xy=10/20=1/2

[meera]

2. Is it possible that there are 53 Tuesdays in a non-leap year? What is the probability?
soln:
The probability is 1/7.
As non leap year will have 52 weeks + 1 day .This 1 day can be any one of seven day

[meera]

7.Co'nvert into Roman Figures Can you write 1789 in Roman figures?
1789=MDCCLXXXIX=1000+500+100+100+50+10+10+10+(10-1)

[keerthi]

3.A friend of mme asked me to write down any multidigit number. But, he put a condition, the number should not end with a zero.I put down the number 96452Then he asked me to add up the five digits and subtract the total from the original number. I did and here is what I got: 96452 - 26 = 96426
He then asked me to cross out anyone of the five digits and tell him the remaining numbers. I crossed out the 2 and told him the rest of the digits. I neither told him the original number nor what I had done with it. Yet 'pop' he told me the exact number I had crossed out.
How do you explain it?
Ans) evry time if we add the no's remaining after striking off one among 5 digits the sum will that number less than a multiple of 9.
In this case after striking 2 remaining digits are =9646
If we add them 9+6+4+6=25
the nearest multiple of nine to 25 is = 27
Hence 25 is 2 less than 27

[keerthi]

7.Co'nvert into Roman Figures Can you write 1789 in Roman figures?


Ans)1000+500+100+100+50+10+10+10+9 =MDCCLXXXIX