Consider the thousands column. The letters represent different digits so, as S is 3, M is 2 and there is a carry of 1 from the hundreds column. Therefore A is 9, U is 0 and there is also a carry of 1 from the tens column. In the units column, O+Y produces a units digit of 3, so O+Y=3 or O+Y=13. However, O+Y=3 requires one of O, Y to equal zero (impossible as U=0) or 2 (also impossible as M=2). So O+Y=13. We can also deduce that N is 8, since, in the tens column, 1 + 3 +N=12. The pairs of digits that produce a sum of 13 are 4 and 9, 5 and 8, 6 and 7. As A is 9 and N is 8, the only possible values for O and Y are 6 and 7. These are interchangeable, but in both cases Y×O=42.