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
Solution (spoil alert)
