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Lights Out

Each press flips a cell and its four neighbours. Turn every light off in the fewest presses — par is the exact optimum, solved over GF(2).

  • Logic
  • Untimed
  • 11 levels

How it plays

Lit cells are ●, dark ones ○. Pressing a cell flips it and the cells directly above, below, left and right. Clear the board.

Two facts make it a puzzle rather than a search: the order of presses never matters, and pressing twice is the same as not pressing. So look for the set of cells to press. Par is the smallest such set; levels grow the board from 3×3 to 5×5 and scramble it harder.

Keys

Space starts and skips ahead · 1–9 pick · Enter submits · Esc stops. On a phone, tap.

What it trains

This practises reasoning about operations that commute and cancel — the idea under parity and linear algebra mod 2. It is practice at this puzzle and claims nothing wider.

Learn

How to get better at lights out: the method, the techniques, what each new level asks of you, and the traps the wrong answers are made of.

Your approach to each question

  1. Before pressing anything, look at the whole board. Cells are named by column letter and row number, so A1 is the top-left and B2 the one diagonally in from it.
  2. Remember the two rules that make it a puzzle: the order of presses never matters, and pressing a cell twice is the same as not pressing it. You are looking for a set of cells, each pressed once.
  3. Find the shapes a single press makes — a plus of five in the middle, a T of four on an edge, an L of three in a corner — and work out which presses, laid on top of each other, give the lit pattern you see.
  4. Press only when you know the whole set. Par is the smallest set, so with no extra presses allowed a single wasted press puts you over par.

Techniques and tricks

  • Read the plus

    A press flips its own cell and the four beside it. A lone lit plus, T or L is one press at its centre — the middle of the plus, the middle of the T’s bar where the stem joins it, the corner of the L.

    e.g. Lit B1, A2, B2, C2 and B3 on a 3×3: press B2 once

  • Overlaps cancel

    Two presses side by side each flip the other’s cell, so both centres end up dark. Look for a pattern with two dark cells inside it where two pluses meet.

    e.g. B2 and C2 together leave B1, C1, A2, B3 and C3 lit — B2 and C2 themselves stay dark

  • Work from a corner

    Only three presses touch a corner: the corner and its two neighbours. A lit corner needs an odd number of those three, a dark corner an even number. Settle the corners first, then the edges.

  • Chase the lights down

    Row by row from the top, press the cell directly below each lit cell; this clears every row but the last. Whatever stays lit in the last row tells you which top-row cells needed pressing. It always works, but costs more presses than the fewest.

  • Count the lights

    An interior press changes 5 cells, an edge press 4, a corner press 3. A board of 3 lit cells in an L in a corner is one corner press, not two edge presses.

As the levels climb

  • The ladder starts on a 3×3 scrambled by one press. Then it alternates: the board grows to 3×4, then a second scramble press; 4×4, then a third; 4×5, then a fourth; 5×5, then more scramble presses up to seven.
  • On the small boards, each scramble press is still visible as a shape. From three or four presses the shapes overlap and cancel, so look for dark holes inside lit areas: those are often where two presses met.
  • On 3×3, 3×4 and 4×5 boards exactly one set of presses clears each board. On 4×4 there are 16 different sets and on 5×5 four; par is the smallest, so a set that works can still be over par — look for a lighter one before pressing.
  • There is no clock. The only limit is par; going over it still earns part credit, par divided by the presses you took.

Traps to avoid

  • Pressing to see what happens. Every press counts toward par, and undoing it costs a second press. Work the set out first.
  • Pressing the lit cell instead of the centre of its shape. To clear a lit T on the top edge, press the cell where the stem meets the edge, not the cell at the bottom of the stem.
  • Chasing when par has no slack. The chase always clears the board but usually takes more presses than the fewest. Use it only with “Extra presses allowed” raised, or to check your answer in your head.
  • Reading a column letter as a row. B3 is column B, row 3 — the moves list names cells the same way, so check both parts before you press.

How to practise

  • Set “Largest board” to 3 while you learn to read single and double presses, then raise it to 4 and 5.
  • Raise “Extra presses allowed” to 3 or more to practise chasing the lights; lower it back to 0 once you can read the set on sight.
  • Before each press, say the whole set aloud — “B2, C2, A3” — and only then press. It stops trial-and-error.
  • When you miss par, read the smallest set in the working and find each of its presses as a shape on the starting board.

Levels

It is untimed unless you turn the clock on. There are 11 levels with the default settings, and the counter stops at the real top. Your level is judged on your last ten answers, every ten: 90% moves you up, below 80% moves you down, which holds most people near four in five right.

All of it is in the settings beside Start — how many answers a judgement looks at and how often it recalibrates, the thresholds, the time, which questions, how many options, and whether you see each verdict at once or review them together at the judgement. You can also jump to any level.

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