In the cryptarithmetic (alphametic) puzzle COCA + COTA = OASIS, each letter…

Concept: A cryptarithmetic (alphametic) puzzle replaces every digit of a column addition with a letter; each letter must stand for one fixed digit (0-9), no two letters share a digit, and the sum must hold true column by column exactly as in ordinary addition, including every carry generated. The way to crack it is to work from the units column outward, carrying each column's carry into the next, and use structural clues — such as a repeated digit position or an extra digit appearing in the sum — to pin values down quickly.

Applying it here:

1. COCA and COTA are 4-digit numbers, but OASIS has 5 digits, so their sum overflows into a new digit. That new leading digit is exactly the carry out of the thousands column, so O equals that carry — meaning O = 1 (the only possible carry from adding two digits plus a carry-in).

2. In the hundreds column, the digits added are O and O (from the O in each addend), plus any carry-in from the tens column. Testing carry-in = 0 gives O + O = 1 + 1 = 2, which fits the hundreds digit of the answer, S = 2, with no carry generated into the thousands column.

3. In the units column, A + A must end in the digit S = 2. Since O already equals 1, A + A = 2 is impossible without reusing that digit, so A + A must instead equal 12, giving A = 6 and a carry of 1 into the tens column.

4. Revisiting the thousands column: C + C plus the carry-in of 0 (from the hundreds column) must end in A = 6, while also producing the carry-out of 1 that fixes O = 1. The only digit satisfying both is C = 8, since 8 + 8 = 16.

5. In the tens column, C + T plus the carry-in of 1 (from the units column) must end in I, with no further carry (since the hundreds-column carry-in was already fixed at 0). With C = 8, this gives 8 + T + 1 = I, and since I must be a single digit, T = 0 and I = 9.

6. The six letters now hold the distinct digits O = 1, S = 2, A = 6, C = 8, T = 0, and I = 9 — all different, as the puzzle requires.

Cross-check: Substituting these digits back: COCA = 8186 and COTA = 8106, and 8186 + 8106 = 16292, which is exactly OASIS = 1 6 2 9 2. The equation holds column by column, confirming the assignment.

So S + O + T + I + C + A = 2 + 1 + 0 + 9 + 8 + 6 = 26.