FORTY + TEN + TEN = SIXTY, where each letter stands for a unique digit from…

Concept: In a cryptarithmetic puzzle, every distinct letter represents a unique digit from 0-9 (no two letters share a digit, and a leading letter can never be 0). Such puzzles are solved column by column starting from the units place, carrying forward exactly as in ordinary addition, and using the bound on each column's maximum possible sum to pin down individual digits.

Application:

1. Units column: Y + N + N = Y (mod 10), so 2N is a multiple of 10, giving N = 0 (with no carry) or N = 5 (with a carry of 1). N = 5 is ruled out below because it leaves the tens column with no valid digit for E, so N = 0.

2. Tens column: T + E + E + carry = T (mod 10), i.e. 2E + carry is a multiple of 10. With N = 0 the carry here is 0, so 2E = 10, giving E = 5 and a carry of 1 into the hundreds column.

3. Thousands column: O + (carry from hundreds) = I (mod 10), and this column must itself carry 1 into the ten-thousands column - otherwise F and S would be forced to be equal, which is not allowed.

4. Since digits 0 and 5 are already used (by N and E), and the maximum possible carry out of the hundreds column is 2 (as the next step confirms), O + carry must reach at least 10 using the largest remaining digit for O; this forces O = 9 with a hundreds-column carry of 2, giving O + 2 = 11, so I = 1 and a carry of 1 passes into the ten-thousands column - this is confirmed together with the full cross-check below.

5. Hundreds column: R + T + T + 1 = X (mod 10), and this column's carry into the thousands place must equal the 2 assumed above. Among the digits still available, R = 7 and T = 8 are the pair for which this carry comes out to exactly 2 (7 + 8 + 8 + 1 = 24, carry 2, X = 4) while also leaving a consistent set of digits for F, S and Y in the final step - the full cross-check below verifies this is right.

6. Ten-thousands column: F + 1 = S. The digits used so far are 0, 1, 4, 5, 7, 8, 9, leaving only 2, 3, 6 for F, S and Y. F + 1 = S is satisfied by F = 2 and S = 3, which leaves Y = 6.

This gives the complete digit map:

Cross-check: FORTY = 29786, TEN = 850 and TEN = 850. Adding these as plain numbers, 29786 + 850 + 850 = 31486, which reads S I X T Y = 3 1 4 8 6 - exactly SIXTY. The digit map is confirmed.

So S + I + X + T + Y = 3 + 1 + 4 + 8 + 6 = 22.