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Were you able to transmongrify a pack of dogs?

On Page 50 of the January Bulletin, in an article about Elizabeth Sherr Sklar ’63 and Jessica Sklar, we printed a mathematical problem that Jessica developed with Gene Abrams of the University of Colorado. The problem gained quite a bit of attention. Here is that problem again, with the answer below it:

Suppose a mad veterinarian creates a transmogrifier that can convert one cat into two dogs and five mice, or one dog into three cats and three mice, or a mouse into a cat and a dog. It can also do each of these operations in reverse. Can it, through any sequence of operations, convert two cats into a pack of dogs? How about one cat? Answer below.

Answer: Starting with two cats, turn one cat into two dogs and five mice, giving you one cat, two dogs, and five mice. Next, convert two mice into two dogs and two cats, giving you three cats, four dogs, and three mice. Finally, convert three cats and three mice to one dog, giving you zero cats, five dogs, and zero mice.

Alas, if you only start with one cat, you can never convert it to a pack of dogs. (Note that fractional dogs are not allowed, even in science fiction!)

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