(In reply to

Solution by Jer)

I never actually "solved" it.

Within seconds I **"GUESSED"** that 15,18 and 10*k fit.

I also "tried" 25,35 which did not...

It is really amazing that 45 is the only number, that avoided this quick detection..

Nice problem, indeed.

BTW, the statement "*greater than nine*" is irrelevant since the problem refers to numbers which have at least two digits (denoting units and tens).

*Edited on ***March 21, 2016, 2:36 pm**