121. HEADS OR TAILS. Crooks, an inveterate gambler, at Goodwood recently said to a friend,
"I'll bet you half the money in my pocket on the toss of a coin--heads I win, tails I lose." The coin was tossed and the money handed over. He repeated the offer again and again, each time betting half the money then in his possession. We are not told how long the game went on, or how many times the coin was tossed, but this we know, that the number of (1/2)
times that Crooks lost was exactly equal to the number of times that he won. Now, did he gain or lose by this little venture? (2/2)
SOLUTION TO 121. HEADS OR TAILS.
Crooks must have lost, and the longer he went on the more he would lose. In two tosses he would be left with three-quarters of his money, in four tosses with nine-sixteenths of his money, in six tosses with twenty-seven sixty-fourths of his money, and so on. The order of the wins and losses makes no difference, so long as their number is in the end equal.
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