Akari techniques: how to solve Light Up step by step

Technique 1 · basic

Zeros and finished numbers

A 0 is the kindest clue on the board: none of its four sides can hold a lamp, so dot every free tile around it before you do anything else. The same move comes back all through a solve in a quieter form. Every time a number gets its last lamp, it becomes a 0 for the tiles still free around it. A 2 with lamps above it and to its left is finished, and its other two sides are empty. Most players spot the 0s at once and miss the finished numbers, because the lamps that finish them usually arrive as part of some other step.

Dots matter more than they look. A dot doesn't light anything, but it removes a candidate, and the techniques below all count candidates. The dots next to a 0 are often the first sign that a tile further away can only be lit from one direction.

Where to look: every 0 at the start, then every number right after a lamp lands beside it.

Technique 2 · basic

Full numbers: a 4, a 3 on the edge, a 2 in a corner

The opposite case is a number that needs a lamp on every free side it has. A 4 is always full, since it has only four sides. A 3 against the edge of the board has just three sides, so all three take lamps, and a 2 in a corner of the board has two. The same goes for a 3 or a 2 hemmed in by other walls, because a wall is not a free side. What really counts is the lamps a number still needs against the free tiles it has left. A 3 in the open with one side dotted is full too, and so is a 1 with a single free tile.

These lamps are the strongest start a board offers, because each one lights a whole row and column at once. Place them first, then look at what their light has just ruled out.

Where to look: 4s, 3s on the edge, 2s in the corners, and any number whose free sides have been cut down by dots or light.

Technique 3 · basic

Lit tiles hold no lamp

A lamp in another lamp's light breaks the main rule, so a lit tile can never take a lamp. That turns every lamp into long lines of ruled-out tiles: its whole row and column, up to the walls. The game paints lit tiles pale yellow, so you rarely need to dot them, but you do need to count them. A number next to a lit tile has lost that side, exactly as if it were dotted. This is how a lamp at one end of a column decides a number at the other end: the light travels, the number loses a free side, and suddenly it is full.

After every lamp, follow its light to the end in all four directions and look at each number it passes. A 2 with three free sides becomes a 2 with two, and you are back to technique 2.

Where to look: numbers sitting at the end of a beam.

Technique 4 · basic

The only light source

Every tile has to be lit, and a tile can only be lit from its own row or column. So take a dark tile and list its sources: the tile itself, if it is free, and every free tile it can see before a wall. If one source is left, the lamp goes there. The tiles worth checking are the dark ones that have lost options: dotted tiles, tiles squeezed between walls, tiles whose row is already crossed by light. A dot is the best lead, because a dotted tile can't light itself. It needs a lamp somewhere along its lines, and the walls often leave only one place for it.

This technique does most of the work on easy boards, and it stays useful to the last move. When nothing else moves, scan the dark tiles one by one and count their sources. Remember the tiles with two sources: technique 7 works with them.

Where to look: dotted tiles next to walls, and short stretches of tiles closed off at both ends.

Technique 5 · intermediate

The diagonal trick for 3s and 1s

Some numbers can leave exactly one free side empty: a 3 with four free sides, a 2 with three, a 1 with two. You can't tell yet which side stays empty, but you know something about every two sides that meet at a corner: at least one of them holds a lamp. The tile in that corner, diagonal to the number, sees both of those sides along its row and column, so it ends up lit however the number is solved. It can't hold a lamp, so dot it. A 3 in the open dots all four diagonal tiles at once; a 1 with two free sides around a corner dots one.

The trick is at its best when the dot lands on another number's side. In the example, the dot is one side of a 3, and the 3 is suddenly full. Diagonal dots also feed technique 4: a dotted tile still needs light from somewhere, and it often has few sources.

Where to look: 1s on the edge with a wall beside them, and 3s and 2s with exactly one side to spare.

Technique 6 · intermediate

Two numbers that share tiles

When two numbers stand diagonal to each other or one tile apart, some tiles touch both, and each number limits what the other can do there. Read them together. In the example, a 1 and a 2 share two tiles. The 1 allows at most one lamp among them, so the 2 gets at most one of its lamps there and must take the other on the one side the 1 doesn't touch. And since the 2 still needs a lamp from the shared pair, that lamp is the 1's only lamp, so the 1's other sides are empty. Neither number could tell you any of this on its own.

Pairs worth learning by heart: a 1 and a 2 sharing two tiles, two 1s sharing a tile, a 3 diagonal to a 1. For each pair, ask how many lamps the shared tiles must hold at least and can hold at most.

Where to look: numbers diagonal to each other, and numbers with one tile between them.

Technique 7 · intermediate

Would it go dark?

Technique 4 asks where a dark tile's light can come from. This one turns the question around: what would a lamp here take away? A lamp lights, and so rules out, every free tile in its row and column. If those include all the remaining sources of some other dark tile, that tile could never be lit, so the lamp is impossible. In practice, start from the tile at risk: find a dark tile with exactly two sources left, then look for a free tile that sees both of them. A lamp there would take away both sources, so that tile gets a dot.

The shape is easy to see once you know it: one source in the row of the tile at risk, one in its column, and a free tile at the fourth corner of the little square they make. The same check works with numbers: a lamp that would light the last free sides a number needs is ruled out too.

Where to look: dotted tiles with two sources left, one in their row and one in their column.

Technique 8 · advanced

Look ahead: follow a chain

When nothing above moves the board, pick a tile, imagine a lamp on it, and play the basic techniques forward in your head: light, full numbers, only sources. If the chain ends in a contradiction, such as a number with too many lamps, two lamps in each other's light or a tile nothing can light, the lamp was wrong and the tile gets a dot. Imagine the tile empty instead, and a contradiction means it needs a lamp. This is not guessing. You keep only what you have proved, and the imagined lamp never goes on the board.

Good chains are short. Start next to numbers, where one lamp quickly fills or finishes something, and drop the idea if nothing breaks after three or four moves. On Lampwise's hard boards the chains you need are usually only two or three moves long.

Where to look: free tiles that see two sides of the same number.

Common mistakes

• Counting diagonal tiles. A number counts only the lamps on its four sides. A lamp touching it corner to corner doesn't count, which is exactly why the diagonal trick works.
• Lighting a dark tile with the first lamp that fits. A dark tile with two or three sources is no reason to place a lamp. Place one only when a single source is left, or when a number forces it.
• Forgetting that a dot needs light. A dot means no lamp, not lit. Every dotted tile still has to be lit from its row or column, and a dot with no sources left means an earlier step was wrong.
• Letting light pass a numbered wall. Every wall stops light, with or without a number. A lamp on one side of a 1 doesn't light the tiles on its other side.
• Leaving finished numbers open. When a lamp lands next to a number, check whether the number now has all its lamps and dot its other sides at once. A missed dot hides the next step.