Henry Ernest Dudeney/Modern Puzzles/68 - Threes and Sevens

by : $68$

 * Threes and Sevens
 * What is the smallest number composed only of the digits $3$ and $7$ that may be divided by $3$ and $7$,
 * and also the sum of its digits by $3$ and $7$, without any remainder.


 * Thus, for example, $7 \ 7 \ 3 \ 3 \ 7 \ 3 \ 3$ is divisible by $3$ and $7$ without remainder,
 * but the sum of its digits ($33$), while divisible by $3$, is not divisible by $7$ without remainder.


 * Therefore it is not a solution.