A four-digit PIN number

**aabb**, where

**a** and

**b** are distinct digits, is a multiple of

**15.**Which values
of **a** are not possible?

I believe I have the solution. Values that are not possible for a are {0,2,5,8}. In order to be a multiple of 15 the only possible digits for b are {0,5} so the number ends in ..00 or ..55. In addition the PIN needs to be a multiple of 3, so addition of all the digits a+a+b+b can not be a multiple of 3; also a has to be different from b. So a can't be 0 or 5. And checking the resulting possibilities we find that a cannot be {2,8} either since the sum of the digits for the following numbers are not multiples of 3: {2200,2255,8800,8855}.