Today I noticed that $294$ is a multiple of $49$, which is the last two digits of $294$ reversed.
How many other numbers have this property? That is, how many three-digit numbers have a factor which is given by taking the last two digits and reversing them?
- I don't know the answer to this question, but I imagine it must be doable in a relatively neat way without too much case-bashing. No programming answers, please.
- Leading zeros are not allowed. When I say "three-digit numbers" it excludes one- and two- digit numbers, and the two-digit factor shouldn't be a one-digit number.