What Integers Were Used?

Relevant wiki: Cryptogram

Since this is an addition, we can apply a technique from cryptogram called rearrangement of columns , and so the following two cryptograms are equivalent:

$\begin{array} { l l l l l l } & & & & & & \square \\ & & & & & \square & 6 \\ + & & & & \square & 5 & 4 \\ \hline & & & & 3 & 2 & 1\\ \end{array} \qquad \qquad \qquad \qquad \qquad \qquad \begin{array} { l l l l l l } & & & & & & 6 \\ & & & & & 5 & 4 \\ + & & & & \square & \square & \square \\ \hline & & & & 3 & 2 & 1 \; . \end{array}$

The cryptogram on the right can be written as an equation, $6 + 54 + x = 321$ , where $x$ is the 3-digit number to be determined, $x = 321 - 6 - 54 = 261$ . Hence, the values of the boxes (from left to right) are 2, 6 and 1, respectively. Let's double check our result by substituting these numbers into the original addition:

$\begin{array} { l l l l l l } & & & & & & \boxed1 \\ & & & & & \boxed6 & 6 \\ + & & & & \boxed2 & 5 & 4 \\ \hline & & & & 3 & 2 & 1\\ \end{array}$

It turns out to be correct!

Our answer is $2 + 6 + 1 = \boxed9$ .

The missing numbers from left to right is 2,6,1 respectively. Therefore the sum is 9.