A POSITIF INTEGER WITH DIGIT 1 OR 2 OR 3

PROBLEM
Each digit of a positive integer is 1 or 2 or 3
Given that each of the digits 1, 2 and 3 occurs at least twice, what is the smallest such integer that is not divisible by 2 or 3?

ANSWER : 1112233
SOLUTION
An integer is divisible by 3 when the sum of its digits is divisible by 3.
Since 2 × (1 + 2 + 3) = 12 is divisible by 3, the digits 1, 1, 2, 2, 3, 3 are not sufficient. 
For the smallest possible integer, we choose an extra ‘1’.
The small digits must be at the front to have the smallest integer overall. 
So the smallest integer made from these digits is 1112233

JMO 2012

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