The Cat and Dog Race Puzzle - Solution

The Puzzle:

The Cat and Dog Race
Many years ago, when Barnum's Circus was of a truth "the greatest show on earth" the famous showman got me [Sam Loyd] to prepare for him a series of prize puzzles.

Barnum was particularly pleased with the problem of the cat and dog race.

"A trained cat and dog run a race, 100 feet straightaway 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 probabilities or possibilities in favor of the one that gets back first?"

Our Solution:

Now, the cat wins, of course. It has to make precisely 100 leaps to complete the distance and return. The dog, on the contrary, is compelled to go 102 feet and back. Its thirty-third leap takes it to the 99-foot mark and so another leap, carrying it two feet beyond the mark becomes necessary. 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 makes quite 67.

But the puzzle turns upon the possibilities of the race. Just let us suppose that the cat is a Sir Thomas cat, and the dog Blanche is one referred to as she ... so the dog really goes 9 feet to the cats 4. As the dog finishes the race in 68 leaps, the cat will have gone but 90 feet and 8 inches.

Puzzle Author: Loyd, Sam

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