If POINT + ZERO = ENERGY, then E + N + E + R + G + Y = ?

In a cryptarithmetic (alphametic) addition, each distinct letter represents one fixed digit (0-9), the same letter always the same digit across the whole sum, and the columns must add up correctly with carries, exactly like ordinary addition. When a k-digit number plus an m-digit number produces a result with one extra digit, the leading letter of the answer must equal that final carry, which from adding two digits (plus at most 1 incoming carry) can only be 1.

1. Align the columns of POINT + ZERO = ENERGY, writing each column's equation with a carry into the next column: units (T+O), tens (N+R), hundreds (I+E), thousands (O+Z), ten-thousands (P), and a new leading digit.

2. Since POINT has 5 digits and ENERGY has 6, the new leading digit equals the final carry out of the ten-thousands column, so E = 1.

3. The ten-thousands column is P + (carry from thousands) = N + 10 x E = N + 10; since P is a single digit and the carry is at most 1, this only balances when N = 0 and P = 9, with a carry of 1 into the new leading digit.

4. The thousands column is O + Z + (carry from hundreds) = E + 10 x (carry into ten-thousands) = 1 + 10 = 11 (since P = 9 needed a carry-in of 1 from the thousands column); trial digits O = 8, Z = 3 satisfy this with no extra carry.

5. The hundreds column is I + E + (carry from tens) = R, with no carry into the thousands column; with E = 1, trial digits I = 5, R = 6 satisfy 5 + 1 + 0 = 6.

6. The tens column is N + R + (carry from units) = G, with no carry into the hundreds column; with N = 0, R = 6, this needs a carry-in of 1 from the units column, giving G = 7.

7. The units column is T + O = Y + 10 x (carry into tens); with T = 4, O = 8: 4 + 8 = 12 = Y + 10, so Y = 2 and the carry into tens is 1, consistent with the previous column.

8. So POINT = 98504 and ZERO = 3168, with every letter (P, O, I, N, T, Z, E, R, G, Y) taking a distinct digit from 0-9.

Verify by direct addition: 98504 + 3168 = 101672, i.e. ENERGY = 101672, which matches E N E R G Y = 1 0 1 6 7 2 letter-for-letter, confirming the assignment.

So E + N + E + R + G + Y = 1 + 0 + 1 + 6 + 7 + 2 = 17.