Lights Out
Press a light, five flip. Darken the board โ every puzzle solvable.
About this puzzle
Every press toggles a light and its four neighbours; the goal is total darkness. Puzzles are built by pressing random cells from a dark board โ so each is solvable in its par number of presses โ with three difficulty levels and your best solve kept on this device.
The two facts that crack it
Lights Out (Tiger Electronics, 1995) hides clean mathematics: presses commute (order never matters) and cancel in pairs (pressing twice equals never) โ so a solution isn't a sequence, it's a SET of cells, and the game is linear algebra over GF(2) wearing a toy's clothes. The practical method those facts enable is light chasing: sweep top to bottom pressing directly beneath every lit cell โ this pushes all light into the last row โ then look up the last-row pattern's fix (each pattern maps to specific top-row presses) and sweep once more. On the classic 5ร5, every solvable position falls to two sweeps. The satisfying corollary of press-cancellation: fumbling randomly can never dig a hole deeper than par + your wasted pairs. Hanoi and the 15 puzzle are the shelf-mates, each hiding different mathematics.
Frequently asked questions
What happens when I press a light?
It and its orthogonal neighbours all toggle โ up to five lights flip per press, fewer at edges and corners. Total darkness wins.
What is the light-chasing method?
Row by row, press beneath every lit cell โ light accumulates in the bottom row โ then apply the known top-row fix for that final pattern and sweep again. Two sweeps solve any solvable 5ร5.
Does the order of presses matter?
No โ presses commute and cancel in pairs, so a solution is a set of cells, not a sequence. This is why the puzzle is secretly linear algebra (over GF(2)).
Are all the puzzles solvable?
Yes โ each is generated by pressing random cells from darkness, so undoing those presses (the par) always works. On a blank 5ร5 grid, some arbitrary patterns wouldn't be.