Numberlink

How Numberlink works

A Numberlink board is a grid with pairs of coloured dots scattered across it. Your job is to join each pair with a single line, and there is one extra condition that turns it from a doodle into a puzzle: every square on the board must end up used. Lines may not cross each other, and no square may be shared by two colours.

That coverage rule is what most people miss on their first board. Joining every pair is usually easy — the dots are often only a few squares apart, and a direct route between them is nearly always available. But a direct route leaves empty squares behind, and a board with an empty square is not solved, however tidy it looks. The lines have to take the long way round, weaving into every corner, and working out which colour is supposed to fill which region is the actual puzzle.

The board here reports both halves separately as you play, so there is never any mystery about which one you are failing: how many pairs are joined, and how many squares are filled. When both are complete the board is solved, and not before.

How to play

Press on a dot and drag. The line follows your finger or your mouse from square to adjacent square — up, down, left and right only, never diagonally. Release when you are done, or when you reach the matching dot, at which point the pair locks as joined.

You do not need to clear a line before correcting it. Dragging back along a line you have just drawn retracts it a square at a time. Grabbing a line part-way along cuts it back to that point and lets you continue from there. And drawing over another colour's line simply cuts that colour back at the square you took — so you can always draw the route you want and repair the damage afterwards, which is much faster than tidying up first.

On a keyboard, the arrow keys move a cursor around the board. Press Enter on a dot to pick that colour up, and the arrow keys then draw instead of just moving. Press Enter again, or Escape, to drop the colour.

Fullscreen hands the whole screen to the board, so the squares grow as large as the display allows and a long drag can no longer scroll the page; press Escape or the Exit button to leave it.

The four sizes

Difficulty here is grid size and the number of colours, which between them decide how long the average line has to be:

• Easy — a 5×5 board with 4 pairs, so 25 squares to cover.
• Medium — 6×6 with 5 pairs, 36 squares.
• Hard — 7×7 with 6 pairs, 49 squares.
• Expert — 8×8 with 8 pairs, 64 squares.

More colours on a bigger board is not simply harder in one direction. Extra pairs mean shorter lines on average, which makes each individual route easier to see; a larger board with the same number of pairs means long, winding lines that are much harder to plan. The Expert board is the largest and also the most crowded, so it is long lines and a lot of them at once.

Move count and par

Every board shows a move count next to a par. A move is one action: picking a colour up, or extending a line by one square. Par is the number of squares on the board — because a flawless solve picks each colour up exactly once and then steps into every remaining square exactly once, and those two counts always add up to the board's size.

So par on the Easy board is 25, and on Expert it is 64. Beating par is impossible; matching it means you drew every line correctly first time, with no retraction and no correction. It is a much harder target than finishing.

Every board has exactly one answer

Boards are generated rather than drawn from a fixed set, so you will not run out. Each one is checked by a solver before you ever see it, and only boards with a single solution are kept — if there were two ways to cover the grid, the puzzle would reward guessing instead of reasoning, which is the difference between a Numberlink and a maze.

The generator works by building a full covering set of paths first and then asking whether any other set of paths would have joined the same dots and covered the same board. Most candidates fail that test and are thrown away, which is why the dots end up where they do: their positions are a consequence of the answer, not a starting point.

The daily board

Daily mode deals from today's date rather than at random, so everyone playing the same size on the same day gets the same board, and restarting re-deals it identically instead of rolling a new one. It resets at local midnight, on your own clock rather than a server's.

Everything here runs in your browser. Your board is saved locally so you can close the tab and come back to it, nothing is uploaded, and the whole tool works offline once the page has loaded.