A new December and a new bunch of puzzles from mscroggs.co.uk.

We’re looking for a 2 digit number, ab (and the product ab * ba). It can’t be a 1 digit number, a, because a * a wouldn’t have 3 digits. It can’t be a 3 digit number, abc, because abc * cba would have at least 5 digits.

Also, ab is a square. It could be 16, 25, 36, 49, 64, 81. Going through these manually shows 16 * 61 = 976 is the only 3 digit number.