It's Math Time!
RAY: Here's the answer. Let's start by looking at what we know. For C-A-B and A-B to end with the same digit B, B must be zero, one, five, or six.
Six sixes are 36, five fives are 25. One times one is one. And since C-A-B is less than a thousand, A-B must be less than 32 because 32 squared is one thousand twenty-four.
So there are only nine possibilities then for A-B. And we narrowed it down from 99 to 9. It can be 10, 15, 16, 20, 21, 25, 26, 30, or 31. Those are the only nine possibilities, and we eliminate a bunch of them right away. Ten, twenty, and thirty we eliminate because 10 squared is a hundred, it would have to be 110. Twenty squared is 400 and 30 squared is 900. Fifteen is out because it's 225.
The only one that works is 25. If A-B is 25, then C is 6. 625 is the square of 25. Not bad, huh?
TOM: Wow, yeah, that's not bad.
RAY: Who's our winner?
TOM: The winner this week is Matthew Phelps from San Clemente, California, and for having his answer selected at random from among all the correct answers that we got Matthew's going to get a $26-gift certificate to the Shameless Commerce Division at cartalk.com with which he can get our latest four-CD set featuring four of our all-time favorite shows, The Field Guide to the North American Wacko.
RAY: Congratulations, Matthew!
[ Car Talk Puzzler ]