From the multiplication below, What is the value of N + A + M + E? H E x E H…

In a cryptarithmetic (alphametic) multiplication, each distinct letter stands for one fixed digit (0-9), and every occurrence of the same letter — in the multiplicand, in each partial product, and in the final product — must take that same digit throughout. Such puzzles are cracked using place-value clues: a partial product that reproduces the multiplicand unchanged tells you the multiplier digit used was 1, and the number of digits in each partial product bounds the possible values of the remaining letters.

1. The first partial-product row is "H E" — identical to the multiplicand "H E" itself. A number stays unchanged when multiplied only by 1, so H = 1.

2. Substituting H = 1, the multiplicand becomes "1E", and the tens-place partial-product row "H H A" becomes "1 1 A" — a three-digit number that must begin with the two digits "1 1".

3. Trying single-digit values of E so that (1E) x E begins with "11": with E = 7, 17 x 7 = 119, which matches "1 1 9" exactly. So E = 7 and A = 9.

4. Multiplying the full two-digit numbers gives 17 x 71 = 1207. This must equal "H N M E" = "1 N M 7", so N = 2 and M = 0.

5. Adding the four letters together: N + A + M + E = 2 + 9 + 0 + 7 = 18.

Cross-check by direct multiplication: 17 x 71 = 1207, and every row of the original layout holds — 17 x 1 = 17 ("H E"), 17 x 7 = 119 ("H H A"), and 17 x 71 = 1207 ("H N M E") — all consistent with H = 1, E = 7, A = 9, N = 2, M = 0.