Arrow Loop Puzzle Generator
An arrow loop puzzle threads a single closed loop through about a third of the grid, moving only up, down, left and right, that must pass through every square that is not shaded and not a numbered clue — there is no square left over unvisited and no square left out of the loop by choice. The remaining squares are shaded, and no two shaded squares may touch. Each numbered clue carries an arrow, and its number says how many shaded squares lie between it and the edge of the grid in that direction. Every grid here is checked to have one answer and no other.
What this generator does
Draws a single closed loop covering about a third of the grid — checked to be the only possible route through those exact squares before anything else is decided — shades or clues everything else, then repairs any clue that leaves more than one answer by turning a shaded square into a clue until the grid is pinned down uniquely.
How to use this tool
- Choose a grid size and how many clues you would like.
- Print or copy the grid; each clue's arrow shows the direction its number counts.
- Shade squares so the count in every arrow's direction matches its number, with no two shaded squares touching.
- Draw one closed loop through every square that ends up neither shaded nor a clue.
- Show the answer to check the finished grid.
Understanding the controls
- Grid
- Five to seven squares a side, same range as the other loop puzzles here.
- Clue density
- Fewer clues leaves more of the grid shaded and is offered up to seven a side; more clues leaves less shaded and is offered up to six, where it was measured to still build quickly.
- Seed (optional)
- Type anything to rebuild the same puzzle later, which is how you reprint a page you have lost. The seed makes the puzzle repeatable; it carries no cryptographic strength and is not a secret.
Common use cases
- A loop puzzle with a second mechanic layered on, for anyone who has run out of plain ones
- A printable page for a puzzle club — the arrow clues read clearly in black and white, so a photocopy loses nothing
- A logic puzzle that mixes counting with drawing a single route
- A change of pace from a pearl loop or a slitherlink
- Reprinting the identical grid later from its seed
How this generator works
An arrow's number only ever reports a count along one line, which turns out to be far weaker information than it looks: a single random shading pinned down zero of forty test grids at five squares a side. Two things fixed that, and both came from measuring rather than guessing. First, a loop covering half a grid or more almost always has more than one route through its own squares before any shading is even chosen — a shape ambiguity no arrow can ever resolve, since an arrow never reports anything about how the loop threads the squares that are left. So the loop is drawn deliberately thin, at under a third of the grid, and checked to be the only possible route through those squares before shading starts at all. Second, once the loop is fixed, every square it leaves behind is shaded unless that would touch an already-shaded neighbour, in which case it becomes a clue — and if the clues that results in still allow a second answer, the square where that answer disagrees with the true shading is turned from shaded into a clue itself, which cannot move the loop, since a clue and a shaded square are equally off it. Repeated until the printed clues allow one answer and no other — measured at zero failures over two hundred seeded attempts at every offered size and density.
Randomness and fairness
The loop, the shading and each clue's direction all come from your browser's cryptographic random source. Giving a seed replaces that source with a repeatable one, so the same puzzle can be printed again; the seed is for reproducibility, not cryptographic strength.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- The grid stops at seven squares a side, and the denser clue setting stops at six — both measured limits: a loop covering much more of the grid than a third almost always has more than one route through its own squares, which no arrow clue can fix.
- Difficulty is not graded. A grid can be led by its arrows from the first move, or need a section worked out before it opens up.
- An arrow's number only ever reports a count, never a shape, so a square between two clues can still take longer to place than the clue count alone suggests.
- A square with no clue nearby is unconstrained by any single arrow, though it is still fixed by the loop and the no-touching rule once enough of the grid is filled in.
Privacy and your data
The loop, the shading and the check that both are unique are all done entirely in your browser. Nothing you type as a seed, and no puzzle made from it, leaves the device.
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