Apologies if this question is a duplicate, but I believe it is not.
If there are three sets of numbers, A, B, and C, and each are integers $1\le n \le9$, occupying the hundreds, tens and unit positions, as follows: ABC; ABC; and ABC,
and when they are added together, they result in a number BBB. i.e.
solve for the integers A, B and C?
So far, solutions seem to be amenable to a 'serendipitous' approach e.g. dividing BBB by three ($999/3$; $888/3$ etc.) until the result matches ABC match (as much as possible).
Obviously, this is not a satisfactorily mathematical solution. I would be grateful if a solution to this specific question using algebra could be suggested.
Also, if the general nature or concept surrounding this problem could be described?