Close, the actual answer is 11 :|

Here is the solution:

As shaon showed, the lucky number must be a 3 digit number.

Suppose the number is

*abc*.

Then

, we have:

ie

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 =)

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