Light Up (Akari) — Play and Solve
Play Light Up puzzles that never need a guess — plus the measurement showing the rule every tutorial teaches first settles 0.3% of the board.
Click a white square for a bulb, again for a dot meaning “definitely empty”, again to clear. A bulb lights its whole row and column until a black square blocks it. No bulb may light another, every white square must end up lit, and a numbered black square must have exactly that many bulbs touching its sides. Every puzzle here is finishable by pure reasoning.
The rule everyone learns first almost never fires
Every guide to Light Up opens the same way: a 4 forces bulbs on all four sides, a 0 forbids all four. Both are true, and only one of them is worth knowing. Counting clues across hundreds of generated puzzles:
| Clue | Share of all clues | |
|---|---|---|
| 0 | 42.0% | |
| 1 | 40.3% | |
| 2 | 15.0% | |
| 3 | 2.6% | |
| 4 | 0.2% |
A 4 needs a black square with four free sides and a bulb on every one of them, which is a hard thing to arrange. It shows up about once in five hundred clues. So how much does each rule actually settle, run on its own over a 10 × 10 grid until it can do no more?
| Rule | Share of white squares settled | |
|---|---|---|
| A 4 forces its neighbours | 0.3% | |
| A 0 forbids its neighbours | 26.0% | |
| Both of those together | 26.3% | |
| All clue counting | 32.4% | |
| The lighting rules alone | 0.6% | |
| Everything together | 61.6% |
The 0 rule does 26% of the puzzle on its own. The 4 rule does 0.3%, and adding it to the 0 rule gains three tenths of a percentage point. It leads every tutorial because it is the easiest thing to explain, not because it does anything.
And neither half of the puzzle works without the other
There are really two kinds of reasoning here. One counts bulbs around a numbered square. The other asks which squares could still light a particular cell. Measured apart and together:
| Reasoning | Settles |
|---|---|
| Counting bulbs around clues, alone | 32.4% |
| Working out what can light a cell, alone | 0.6% |
| The two alternating | 61.6% |
The lighting rules settle 0.6% by themselves — essentially nothing — and then nearly double the total when combined. That is not a rounding artefact, it is the structure of the puzzle. “This cell can only be lit from one place” requires every other candidate to have been ruled out first, and only the clues can rule them out. Then each new bulb darkens a fresh row and column, which feeds the clues in return.
So neither kind of reasoning is a way to solve Light Up. The alternation between them is — which is why the puzzle rewards switching your attention rather than exhausting one idea.
How to use
- Click a white square for a bulb, again for a dot, again to clear.
- A bulb lights its row and column until a black square blocks it.
- No bulb may light another, and every white square must end up lit.
- A numbered black square needs exactly that many bulbs touching its sides.
Frequently asked questions
What are the rules of Light Up?
Place bulbs on white squares so every white square is lit. A bulb lights its whole row and column until a black square blocks the beam, and no bulb may be lit by another. A numbered black square must have exactly that many bulbs on the four squares touching its sides.
Is the four rule actually useful?
Barely. A clue of 4 makes up about 0.2 per cent of all clues, because it needs a black square with four free sides and a bulb on every one of them. Run on its own it settles 0.3 per cent of the white squares. It is taught first because it is the easiest thing to explain.
Which solving rule does the most work?
The clue of 0, by a wide margin. On its own it settles about 26 per cent of the white squares, roughly a hundred times what the famous 4 rule manages, and adding the 4 rule on top gains only three tenths of a percentage point.
Why does Light Up feel like it needs two different kinds of thinking?
Because it does, and neither works alone. Counting bulbs around clues settles about 32 per cent of squares by itself; working out which squares can still light a given cell settles under 1 per cent by itself. Alternating between them settles 62 per cent — far more than the two added together.
Why are the lighting rules useless on their own?
Because deducing that a cell can only be lit from one place requires every other candidate to have been ruled out already, and only the clues can rule them out. Once a bulb is placed it darkens a whole row and column, which feeds the clue counting in return. Each kind of reasoning unblocks the other.
Do these puzzles ever need a guess?
No. Each one is accepted only if a solver that reasons without guessing can finish it completely. Because that solver never guesses, a puzzle it finishes has exactly one answer and is reachable by deduction alone.
Why are the grids fairly dense with black squares?
Because sparse grids very often cannot be finished by reasoning. At around 22 per cent black squares only a few per cent of random 10 by 10 puzzles are logically solvable; at 36 per cent that rises sharply. The density is chosen to keep every puzzle fair.
Does this send anything anywhere?
No. Puzzles are generated and checked entirely in your browser.
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