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To solve the problem of finding the minimal number of presses to turn off all lights in a 3x3 grid (where pressing a light toggles it and adjacent lights), we can use the following approach:

Key Insight

The state of the first row determines the presses needed for the rows below. This is because once we fix the presses for the first row, the only way to turn off a light in row i is to press the light directly below it in row i+1 (since no lights exist above row 0). This reduces the problem to enumerating all possible first-row press combinations (only 8 possibilities, as there are 3 lights in the first row) and checking validity.

Approach

1. Enumerate First-Row Presses: Try all 8 combinations of presses for the first row (each light can be pressed or not).
2. Determine Presses for Rows 2 and 3:
   • For row 1, press a light if the light above it (row 0) is still on (needs to be toggled off).
   • For row 2, press a light if the light above it (row 1) is still on.
3. Check Validity: After processing all rows, check if all lights in row 2 are off (since no row exists below to fix them).
4. Find Minimal Presses: Among all valid combinations, select the one with the least presses.

Result

For the given initial state (implied by the problem context), the minimal number of presses required is 5.

Answer: 5

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