Numbered walls in Light Up (Akari) do not count diagonal lights — a numbered black square counts only the lights placed in its four orthogonal neighbors, the cells directly above, below, to the left, and to the right of it. Diagonal placements, no matter how close they look on the grid, are completely ignored by the clue. This is one of the most common sources of confusion when a player is learning the rules, because in many other placement puzzles (Battleships, Tents, Heyawake) a diagonal touch counts as contact. In Light Up it does not. The printed number on a black wall equals exactly the count of lights in those four adjacent cells, and a light placed in any of the four corner-touching cells contributes zero to the clue. The rule is fixed across every Light Up puzzle, including the Lizely 5 by 5 board, and is part of the public Akari rule set that Nikoli publishes for the genre. Once this fact is clear, numbered walls become very direct constraints rather than mysterious hints.
What a Numbered Wall Actually Counts in Light Up
The four orthogonal neighbors are the only cells that a numbered wall inspects. Concretely, a printed 2 on a black wall means exactly two of those four cells contain a light. A printed 0 means none of them contain a light, and no light may legally be placed in any of the four neighbors because that would instantly violate the clue. A printed 4 means every one of the four straight neighbors is lit. The general Light Up literature describes clues ranging from 0 through 4; the Light Up (Akari) tool on Lizely uses two 1 clues and two 2 clues, which keeps the puzzle compact and lets the orthogonal rule do most of the work.
Because the rule is purely local, a player can read each numbered wall in isolation. There is no need to reason about the rest of the board to satisfy a clue; the four straight neighbors either contain the right count of lights or they do not. This makes the orthogonal rule the most reliable entry point when solving any Light Up board, especially a small one. The four diagonal corners around a numbered wall remain fully available for any legal purpose, including holding lights that illuminate the rest of the grid, provided they do not cause two lights to share an unobstructed row or column.
The Lizely 5 by 5 Board and Its Four Numbered Walls
The fixed Lizely board has twenty white cells, four numbered walls, and one unnumbered wall. The four numbered walls sit roughly in the four quadrants of the grid, and each one only inspects its four orthogonal neighbors. The disclosed solution places lights at cells 2, 6, 9, 10, and 23 in zero-based order, which corresponds to row 1 column 3, row 2 column 2, row 2 column 5, row 3 column 1, and row 5 column 4. The clue 2 in the upper-left touches the row 1 column 3 light and the row 2 column 2 light and ignores the row 3 column 1 light, which sits diagonally beneath them. The clue 2 below it touches the row 2 column 2 light and the row 3 column 1 light and ignores the row 1 column 3 light, which sits diagonally above. The clue 1 near the upper-right only sees the row 2 column 5 light, and the lower clue 1 only sees the row 5 column 4 light.
None of those four clues ever inspects a diagonal neighbor, and that is why the configuration scores exactly 1,000 with no clue errors. The unnumbered wall in the same board is purely a beam blocker; it has no clue constraint at all, so any number of lights can sit in any of its orthogonal neighbors, including zero. Diagonals adjacent to the unnumbered wall are similarly unrestricted. The board is intentionally small so the orthogonal-only rule can be checked by inspection, which is a useful training condition for newcomers who are still internalizing the difference between clue adjacency and ray visibility.
How to Place Lights Using the Orthogonal-Only Rule
- Locate every numbered black wall and write down its four orthogonal neighbors. Skip the diagonal corners entirely; they do not participate in the clue.
- For a 0 clue, mark all four orthogonal neighbors as X with the Mark empty control, the X keyboard shortcut, or a tap that cycles through X. A light in any of those four cells would immediately fail the clue.
- For a 4 clue, place a light in each of the four orthogonal neighbors using Place light, the B or Space key, or a tap. The clue is then satisfied by construction and cannot fail later.
- For a 1, 2, or 3 clue, count how many orthogonal neighbors are already forced to contain lights because of other constraints, then mark the remaining candidates as X until only the right number remain. Diagonal candidates remain available for any other role.
- Extend each confirmed light as a beam along its row and column, stopping at black walls and the board edge, and mark every illuminated white cell. Continue until all 20 white cells are either lit or marked as light or X.
- When every white cell carries either a light or an X, choose Check board or press Enter. A strictly valid board finishes at exactly 1,000 points; a full but invalid board records one mistake and leaves the conflicts highlighted for revision.
Diagonal Confusion in Similar Puzzles
The diagonal question is not specific to Light Up. Several placement puzzles in the same family treat diagonals differently, and a player moving between them can easily carry over the wrong assumption. The table below summarizes how the Lizely puzzle catalog handles diagonal adjacency for clue counting or separation rules. None of the entries below should be confused with Light Up's orthogonal-only clue behavior.
| Puzzle | Diagonal rule for clue or separation | What a diagonal placement does |
|---|---|---|
| Light Up (Akari) | Diagonals are ignored by numbered clues. | Counts zero toward the wall's number. |
| Battleships | Diagonals must be empty around each ship. | Two ships in diagonal corners of a 2x2 area would violate the no-touch rule. |
| Tents | Diagonals must be empty around each tent. | A tent next to its tree but with another tent in a diagonal corner is illegal. |
| Heyawake | Diagonals do not affect room shading rules. | Black cells may sit diagonally next to each other without breaking any rule. |
The table makes the contrast explicit: in Battleships and Tents, diagonals are restricted even though the count clues themselves are orthogonal, while in Heyawake diagonals are again ignored. Light Up sits in the Heyawake family in this respect — the clue cares only about the four straight neighbors. Nikoli's Akari rule page describes the same constraint in the original wording, which has not changed since the puzzle's introduction.
Solving Approach That Exploits the Orthogonal-Only Rule
The orthogonal-only nature of the clue makes numbered walls very powerful solving aids. Start by listing the four straight neighbors of every numbered wall and determining which of them are still legal light candidates after the other rules have spoken. Cells that would force the clue over its printed limit become X marks immediately, and that pruning step is exact: no future solving step can revive a cell that has been excluded by a clue cap. From there, trace every dark corridor, a contiguous stretch of unlit white cells with no numbered wall or board edge breaking it, and find the cells that have only one possible source of illumination. Drop a light there, and confirm that the new light does not share an unobstructed row or column with any other light already on the board.
Because diagonals never contribute to clue counts, the solver can safely ignore them when checking clue math. The only place diagonals matter in Light Up at all is the implicit "two lights may not share a row or column" rule, which operates on straight lines rather than diagonal contacts. That separation is one of the cleanest parts of the puzzle's design: ray visibility runs along rows and columns, clue adjacency runs along the same four straight neighbors, and the diagonal simply carries no rule weight. Players who internalize that separation stop second-guessing the four corners around every numbered wall, and the rest of the board tends to fall into place once the orthogonal counts are pinned. For a deeper walkthrough of the score route, see the Akari Puzzle Rules on a 5×5 Board: Score 1,000 Points guide, which applies the same orthogonal reasoning to a complete run.
If you're weighing options, How to Avoid Common Mistakes in Lights Out covers this in detail.