RAY: This puzzler came from a fellow named Barry Lawber, and if I'm not mistaken, I think this letter was dated 1996. You're given $100 and told to spend it all purchasing exactly one hundred animals at the pet store. Dogs cost $15, cats cost a buck and mice as you might expect are 25 cents each. So you have to spend exactly a hundred bucks, you have to buy a hundred animals and you have to purchase at least one of each animal. And of course mice have to be purchased in multiples of four, otherwise you are never going to wind up with an even hundred dollars. So, the question is: how many of each animal do you have to purchase to spend exactly a hundred dollars and get exactly a hundred animals?
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 3:30am?
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.
[ Car Talk Puzzler ]
