Numberlink Solver, Step by Step
Pick a colour, then tap the two squares where its dots are. Tap a dot again to remove it.
How to use the numberlink solver
Set the width and height to match your puzzle. Pick a colour and tap the two squares that hold its dots, then the next colour, and so on; numbered puzzles work the same way, with a colour for each number. Press Explain the next step: the solver draws the lines that are certain, outlines what changed, and says why. Show the answer draws them all at once and checks the solution is the only one. It works for any puzzle of this kind up to 15 by 15 with up to 16 colours, including the coloured-dot puzzles in apps such as Flow Free; Greg Puzzles is not affiliated with Flow Free or its makers.
The rules of numberlink
Join each pair of matching dots with a line. Lines run from square to square, up, down, left or right, and never cross or share a square. Every square on the board is used. In numberlink, and in well-made puzzles of this kind generally, a line also never runs alongside itself: two squares of the same colour that touch are always joined directly. The solver uses that rule, and drops it only if there is no other way to fill the board.
How to solve numberlink, step by step
Follow the forced moves. A dot, or the end of a line, with only one open neighbour has to go there. Look for squares with two ways in. Every square is used, so an empty square with only two open sides has a line running straight through it. Corners are the classic case. Never let a line touch itself. When two squares of one colour sit side by side, the line joins them. Keep colours apart. A line cannot step onto a square another colour already holds, or close a loop. When those run out, the solver tries a move both ways and keeps the one that does not break a rule.
How it was checked
The solver was run on all 120 puzzles of the daily numberlink. It found each stored answer and found it to be the only one, and every step it explained was checked against those answers: it never drew or crossed out a line wrongly. 118 of the 120 were explained from start to finish. It was also run on bigger boards, from 9 by 9 to 14 by 14, with the same result.
More logic puzzles
There is a new daily numberlink every day. The Zip solver draws a single line through a grid, and the slitherlink solver explains its steps the same way. For a puzzle you hold in your hands, see our brain teasers. There are more solvers on the puzzle tools page.
Frequently Asked Questions
How do you solve numberlink?
Follow the forced moves: a dot or line end with only one open neighbour must go there, and an empty square with only two open sides has a line running straight through it, which makes corners a good place to start. Keep colours apart, never close a loop, and never let a line run alongside itself.
What are the rules of numberlink?
Join each pair of matching dots or numbers with a line that moves up, down, left or right. Lines never cross or share a square, and every square on the board is used.
Is numberlink the same as Flow Free?
The puzzle is the same: Flow Free is an app version of numberlink with coloured dots instead of numbers. The solver takes either.
Can a line run next to itself?
In numberlink, no: a line never runs alongside itself, and well-made puzzles never need it. The solver uses that rule, and only drops it when there is no other way to use every square.
Does every numberlink have one solution?
A well-made one does. The solver checks, and says if the dots you placed allow more than one.