# The cat and dog race

Many years ago, when Circus Bamum was really “The World's Greatest Show,” the owner asked me to prepare for him a series of prize puzzles for advertising purposes. They were well known due to the great prizes offered to anyone who could solve them.

Bamum was particularly pleased with the problem of the cat and dog's career and made it known everywhere that an April first would give the answer and deliver the awards or, as he himself said: “there will be no more cat locked up but released, for the benefit of the most interested ”.

The riddle said the following:

A trained cat and dog run a hundred foot race and then return. The dog advances three feet in each stride and the cat only two, but Marlene strikes three times for every two of Terry.

With these conditions What are the possible results of the competition?

#### Solution

The cat wins naturally. You have to take exactly 100 jumps to travel the full distance and return. The dog, on the other hand, is obliged to travel 102 feet and return since his thirty-third jump takes him to the 99-foot mark so that a further jump is necessary that will take him two feet beyond the end of the travel. In total the dog must make 68 jumps to travel the path. But since it advances to 2/3 of the speed of the cat, when the latter completes the 100 jumps the dog does not reach 67.

But Barnum had an ace up his sleeve to avoid delivering the prize. Suppose the cat's name is Terry and that the dog was a dog named Marlene. The phrase "Marlene gives three jumps for every two of Terry" would mean then that the dog would travel 9 feet at the same time that the cat would advance only 4 in this way while the dog would finish the race in 68 jumps the cat would only have traveled 90 feet and 8 inches and the winner would therefore be the dog.