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?

15 = 5 * 3

Therefore, all PIN candidates are multiples of both 3 and 5.

Multiples of 5 end in 0 or 5 ==> b = 0 or 5

To find the "possible" values of a, we need only find numbers aa00 and aa55 which are __evenly divisible__ by 3. The rest are "not possible."

A quick scan for "not possible values" of a finds:

a = 2, 3, 5, 6, 8, 9 when b = 5

and a = 1, 2, 4, 5, 7, 8 when b = 0