Cryptograms (Problem 1)

The only number which when multiplied by $3$ results in a number whose unit's place digit is the same as that number is $5$ . We have $5\times 3=15$ , and so $1$ is carried over. Therefore the unit's place digit of $3G$ is $4$ , and therefore $G$ is $8$ . Then $2$ is carried and $3R$ must have a unit's place digit $3$ , and it has to have a single digit. Therefore $R=1$ , and $\overline {BBB}=\boxed {555}$ .

Well seriously, the only digit that when $\times 3\mod 10$ gives the same number and is not $0$ is $5$ . So the answer is $\color{#3D99F6}\boxed{555}$ .

$\large{\begin{array}{ccccccc} & 1& 8&5 \\ & 1& 8&5\\ + & 1& 8&5\\ \hline & 5 & 5&5 \end{array}}$

where $B = 5$ , $R = 8$ and $G = 1$