What is the smallest integer which...

...when multiplied by 3 gives a number consisting of only 4's?

Puzzle Copyright © Kevin Stone

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Hint

Try working backwards.

Answer

148.

Reasoning

A number that is divisible by 3 has digits that add up to a number that is also divisible by 3 (for example, 123 is divisible by 3).

So we can look for the first number where 4 + 4 + 4 + 4 + 4 + ... is divisible by 3, which is 4 + 4 + 4, and 444 ÷ 3 = **148**.

Alternative Reasoning

Let's try the possible answers in order:

4 ÷ 3 = 1.3333

44 ÷ 3 = 14.6666

444 ÷ 3 = **148**

Double-Checking

148 x 3 = 444.

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