Sam Loyd devised this puzzle for P.T. Barnum:
A trained cat and dog run a race, one hundred feet straight away and return. The dog leaps three feet at each bound and the cat but two, but then she makes three leaps to his two. Now, under those circumstances, what are the possible outcomes of the race?
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As we might have expected, it’s a trick question. It appears at first that the race will end in a tie, as the two animals are covering ground at the same rate. The trouble occurs at the far end of the course. The cat, which covers 2 feet at a bound, can turn around neatly at the halfway point. The dog, which covers 3 feet, cannot: It will arrive at the 99-foot mark and then must make an additional leap to get past the same point.
“In all, the dog must make 68 leaps to go the distance. But it jumps only two-thirds as quickly as the cat, so that while the cat is making 100 leaps the dog cannot make quite 67.”