Here is the solution:
As shaon showed, the lucky number must be a 3 digit number.
Suppose the number is abc.
Then , we have:
Note that as b and c are the ten's digit and unit's digit respectively, then
So the maximum is and therefore the maximum a is
So we must only check for
For a = 1, we have
For a = 2, we have
For a = 3, we have , and there are no other solutions.
Hence there are exactly 11 lucky numbers, namely,
We should post up easier questions first just to get the marathon going =)