Numbrix Puzzle Maker

How to solve it

Fill every square so the numbers run 1, 2, 3 … to the end in an unbroken chain, with each number touching the next one above, below, left or right — never diagonally. Work outward from a pair of given numbers that are close together: if 14 and 18 are three cells apart, there is exactly one way to route 15, 16 and 17 between them, and each stretch you fix narrows the next.

⭐The usual clue pattern does not guarantee one answer

Printed Numbrix follows a convention: reveal roughly every fourth number along the path, which works out at about a quarter of the grid. That feels like plenty, and it very often is — but it is not a guarantee, and the gap is not small. Building random paths, applying the convention, and then counting how many answers actually fit:

Between 60% and 85% depending on the board — so on the worst size measured, 40 boards in every hundred built to the convention have more than one valid answer. Anyone generating these by pattern alone and printing the result is shipping ambiguous puzzles at that rate. Every puzzle on this page is counted before it is shown, and only single-answer boards survive.

⚠️And it would be tidier to say the convention degrades as the grid grows — but it does not. The rate moves around without a direction, so the honest claim is that it is unreliable at every size rather than progressively worse, and that column is left unsmoothed.

Where it starts and ends tells you nothing

The two numbers a solver instinctively treats as the anchors are 1 and the last one, because they are the ends of the chain. On their own they are worth nothing at all: across 380 boards at four sizes, a grid given only its first and last numbers had a single answer zero times. Not rarely — never. Between any two cells there are simply too many routes, and fixing both ends of a journey says very little about the road.

This is also why nothing on this page is about whether a path exists. A rectangular grid always has one — snake along the rows and you have built it — so unlike the knight's tour, where existence is the whole question, here existence is free and the entire difficulty is in telling one path from all the others.

Printed puzzles give you about twice what logic requires

The last column of the table is what happens if you strip numbers away for as long as the answer stays unique. A Numbrix holds together on 16% of its cells at 5 × 5, falling to about 12% at 8 × 8 — roughly half of what the convention prints, and a smaller share the bigger the grid gets. That is not an argument for printing minimal puzzles. A minimal Numbrix is technically solvable and genuinely unpleasant, because the chain of forced deductions gets long and thin and one slip costs the whole board. The Hard setting above thins the clues a little way toward that line and deliberately stops well short of it.

⚠️Honest limits: these are random paths from one shuffling method, not the hand-designed paths a human setter would draw, and the minimal column is ten boards per size rather than hundreds because stripping a board to its last removable clue is the slow direction — proving uniqueness with almost nothing given costs about 820 ms a board at 8 × 8. The 7 × 7 and 8 × 8 rows of the main table are measured once and frozen into the page, and the test suite re-derives them so they cannot drift away from the code.