Any of you listen to Car Talk, the auto show by Tom and Ray? It’s a great weekend listen (although thanks to the glory of the Internet, you can hear episodes at pretty much any time from pretty much any place with an internet connection). During each show they have a Puzzler, the answer to which they reveal the following week. Some of the puzzlers have a mathematical bent, like the one from Ray for the week of December 8:

This puzzler is from my mathematical series. Every two-digit number can be represented as AB, where B is the ones digit and A is the tens digit. Right? So for example the number 43, A is 4 and B is 3.

Imagine then that you took this two-digit number and you squared it, AB x AB, and when you did that the result was a three-digit number, CAB.

Here’s the question: What’s the value of C? So, for example if AB is 43, CAB might be 943. Of course this is a totally bogus answer, but you get the idea.

So again, what is the value of C, so that AB(squared)= CAB?

This can be done by brute force, but examples of more elegant solutions are certainly welcome! (Indeed, since the answer has already been posted online, there’s no harm is sharing partial or complete solutions).

*Thanks to Ted for bringing this puzzler to my attention!*