(In reply to Solution
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