Puzzles contest - 14 With answers

[HELP]

1. During my last visit to Las Vegas in the U.S.A., I met a man who was an "inveterate gambler. He took out a coin from his pocket and said to me, 'Heads I win.tails I lose. I'll bet half the money in my pocket.'He tossed the coin, lost and gave me half the money in his pocket. He repeated the bet again and again each time offering half the money in his pocket. The game went on for quite some time. I can't recollect exactly how long the game went on or how many times the coin was tossed, but I do remember that the number of times he lost was exactly equal to the number of times he won. What do you think, did he, on the whole, gain or lose?

2. I had Rs. 1.15 my purse in 6 coins, but I found that I could not give change for a rupee, half a rupee. quarter rupee, ten ~aise or five paise. Which 6 coins did I have?

3. The date 8.8.64, meaning August 8,1964 is a very interesting date, because the product of the first two numbers equals the third. Can you find the year of the twentieth century which gives the maximum dates of this kind?


4. Which is worth more, a bucket full of half a ;overeign gold pie~es or an identical bucket full of 1 ;overeign gold pieces?





5. One day, Mammu set a very interesting problem to 'lle. She pushed a large circular table we have at lome, into the comer of the room, so. that it touched Joth walls and spilled a spot of ink on the extreme ~dge, and she said, 'Mummy here is a little puzzle for ,Iou. Look at that spot. It is exactly eight inches from Jne wall and nine inches from the other. Now tell me :he diameter of the table without measuring it Can you?





Answers
1. The man must have lost. And the longer he went on the -more he would lose-with simpll' calculations. We can draw this'concluslon:

In two tosses he was left with three quarters of his money. .
In six tosses with twenty-seven sixty-fourths of his money, and so on.


immaterial of the order of the wins and losses. He loses money. so long as their number is in the end equal


2. I had one 50 paise coin, one 25 paise coin and four 10 paise coins.



3. Let's consider the year 1948. Fortyeight has the follow-
ing factors:
24 and 2 i.e. 24th of February
4 and 12 i.e. 4th of December
12 and 4 i.e. 12th of April
16and. 3 i.e. 116thofMarch
6and 8 i.e. 6th of August or
8 and 6 i.e. 8th of June
and giving six dates. The years 36, 48, 60 and 72 each
give six dates whereas the maximum number of such


dates is gtven by the year 24 seven occasions
4. The bucke.t full of half sovereign gold pieces are worth more since the denominations of the gold pieces make no difference. What is most important here is the bucket containing half sovereign gold pieces is full of gold whereas the other one is only half full.




5. Double the product of the two distances from the wall and you get 144, which is the square of 12. The sum of the two distanees is 17. and when we add these two numbers, 12 and 17 together and also subtract one from the other, we get two answers 29 and 5 as the
radius, or half-diameter of the table. Naturally the diameter shquld be 58" or to". However,a table of the latter dimensions. cannot be a 'large circular table' and therefore,the table must be 58" in diameter.




Edited by: HELP