Lights Out 5x5: Solve the Board by Chasing Rows

Start with the exact Lights Out 5x5 rules

In classic Lights Out 5x5, pressing a square switches that light and its immediate horizontal and vertical neighbors. An on light turns off; an off light turns on. Edges do not wrap, and diagonal neighbors stay unchanged. You may press an unlit square. The goal is to turn every light off.

ProjectGAMR uses those two-state rules. Its generator starts with an unlit board and applies legal presses, so its starting positions can be solved by reversing presses. That guarantee concerns this generator: an arbitrary arrangement copied from elsewhere may be impossible under the same rules. This guide checks the local implementation as of October 20, 2026.

Chase each lit row into the row beneath it

Number rows from top to bottom and columns from left to right, both from 1 to 5. For every light on in row 1, press the square directly beneath it in row 2. Those presses switch the corresponding row-1 lights off. They may change several row-2 lights; finish the whole first row before making your next decision.

Repeat for row 2 by pressing row 3, then row 3 by pressing row 4, and row 4 by pressing row 5. A press reaches only one row upward, so working downward leaves previously cleared rows alone. After this light-chasing strategy, rows 1–4 are clear. The bottom row may still contain lights because there is no sixth row to chase into.

Match the bottom row to a top-row correction

Read each five-digit pattern left to right. On the left, 1 means a bottom-row light is on. On the right, 1 means press that top-row square once; 0 means leave it alone. Apply the correction to your current board, then chase downward again. These classic 5x5 bottom-row patterns follow John Burkardt's published table, linked below.

If the bottom row is 00000, you are already finished. The seven nonzero cases below cover the other endings of solvable boards with these rules. A different ending calls for checking your transcription, earlier presses and puzzle variant before applying this table.

• Bottom 00111 → press top 00010 (column 4).
• Bottom 01010 → press top 01001 (columns 2 and 5).
• Bottom 01101 → press top 10000 (column 1).
• Bottom 10001 → press top 00011 (columns 4 and 5).
• Bottom 10110 → press top 00001 (column 5).
• Bottom 11011 → press top 00100 (column 3).
• Bottom 11100 → press top 01000 (column 2).

A checked ten-press example

Use this illustrative position: rows 1–4 are entirely off, while row 5 has only columns 3, 4 and 5 on. It is a deliberately constructed example, not a promised starting board in New game. The first chase changes nothing, because the first four rows are clear. Bottom 00111 selects top 00010: press row 1, column 4.

Now chase again. Press row 2 at columns 3, 4 and 5; row 3 at column 2; row 4 at columns 1, 2, 4 and 5; and row 5 at column 2. Including the top correction, those ten presses switch the entire example off. Treat that as a verified solution sequence, not a claim that ten is the minimum possible.

Keep temporary lights separate from mistakes

A useful press can increase the number of lit squares before a later press clears them. Chasing controls which row you finish, rather than greedily reducing the total after every move. Press order does not change the final result for a fixed set of moves, and pressing the same square twice cancels its effect.

ProjectGAMR's New game generates a fresh position; it does not restore the board you were solving. Record the five row patterns or planned coordinates if you want to check a calculation. The move counter measures presses in that attempt. It does not certify that a completed solution is shortest.

Use the method within its stated variant

This lookup is specific to the classic non-wrapping 5x5, two-state board. A three-state light, a wraparound edge or a rule allowing only lit-square presses changes the problem. Do not transfer the correction patterns simply because another puzzle has a similar grid.

On the matching board, the practical routine is consistent: clear four rows, read the bottom, apply its top correction and clear downward once more. The row-by-row invariant makes progress visible even while individual lights switch back on. That is the reusable idea behind the solution.