Cats and Dogs and Mice - Oh My!

Jan 11, 2003

RAY: I happened to find this puzzler the other day in my puzzler folder. It's from Barry Lawber. And it's from July '96.

TOM: I hope he's still alive.

RAY: I hope so too.

Here's his puzzler:

You're given a hundred dollars and told to spend it all purchasing exactly a hundred animals at the pet store. Dogs cost $15. Cats cost a buck, and mice are 25 cents each.

TOM: Let me get this straight. You have to spend exactly a hundred bucks and you end up with exactly a hundred animals?

RAY: Right. The other only other criterion is that you have to purchase at least one of each animal.

The question is, how many of each animal do you have to purchase to equal a hundred animals purchased at exactly a hundred dollars?


RAY: So, here's the equation: D stands for dogs plus C stands for cats plus M stands for mice equals 100.

TOM: That's the equation.

RAY: And then 15 D, a dog costs 15 bucks plus 1 C, cats cost a buck. Plus 0.25 M. Now, as any eighth grader will tell you, you can't solve this because you have two equations and three unknowns, D, C and M.

Well, here's how I solved it. I figured it wasn't going to be five dogs because five dogs would eat up $75 and then you'd only have $25 with which to buy another 95 animals, and it wasn't going to work.

TOM: No.

RAY: And I knew it wasn't zero dogs because that was one of the conditions of the puzzler. So I changed the equation from three unknowns to two. And I wrote new equations. The first one of which is C plus 0.25M equals 85. That assumes one dog. And then the C plus M, now becomes 99. And you do that, and I solve for M.

TOM: Yeah, and what'd you get, what'd you get?

RAY: Eighteen and two thirds mice.

TOM: No good.

RAY: And if you then do it for two dogs, your equation becomes C plus 0.25M equals 70, and when you solve that equation you get a similarly unsatisfactory result. So this is kind of trial and error. And the correct answer turns out to be three dogs, 41 cats and 56 mice.

TOM: Yeah. That's good. I got that answer, too.

RAY: At what, 3:30 am?

TOM: No, I had the answer right away. I just kept thinking there was an elegant way of doing it.

RAY: I'm sure there is an elegant way of doing it.

TOM: There isn't.

RAY: Anyway, who's our winner?

TOM: The winner is Boyce Griffith from Oak Ridge, Tennessee.

Get the Car Talk Newsletter