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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