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Even Digits Multiple Of Nine

Problem

Find the smallest multiple of nine containing only even digits.


Solution

If a number is divisible by nine then the sum of digits must be a multiple of nine.

But if all of the digits are even then they must sum to an even multiple of nine, and the smallest even multiple of nine is eighteen.

Hence we are looking for the most efficient way to write eighteen as the sum of even digits: 2 + 8 + 8. That is, the smallest multiple of nine containing only even digits is 288.

Find the first five multiples of nine containing only even digits.

Problem ID: 327 (05 Jul 2007)     Difficulty: 1 Star

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