Find an assignment of digits (0, ..., 9) to letters so that a given arithmetic expression is true. For example,

What digits can be assigned to the letters S, E, N, D, M, O, R, and Y so that this is a valid addition statement?

What digits can be assigned to the letters D, O, N, A, L, G, E, R, B and T so that this is a valid addition statement?

What are the states, operator and goal for this task?

We can transform this into a set of equations:

But this is not how people solve it. People search: