Find all integers n greater than nine that satisfy
the following:

The integer formed by inserting the zero digit
between the units and the tens digits of n is
a multiple of n.   

(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

Posted by Ady TZIDON on 2016-03-21 14:30:44