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What is the smallest integer, which, when multiplied by 3 gives a number consisting of only 4's?

 [Ref: ZENA] © Kevin Stone

148. 148 * 3 = 444.

It's easiest to work backwards and look for a number consisting of 4's that is divisible by 3:

4 ÷ 3 = 1.3333
44 ÷ 3 = 14.6666
444 ÷ 3 = 148 - as required.

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