Determine the smallest positive integer whose first 6 multiples (including itself) contain the digit 2.

Just because I could, I solved this problem for an easier case, namely base 3. In base 3, the solution is 102 (base 3).

The first six multiples are

102 (base 3)

211 (base 3)

1020 (base 3)

1122 (base 3)

2001 (base 3)

2110 (base 3)

102 (base 3) = 11 (base 10)