How to play Number Link
A grid with pairs of matching numbers. Draw a line between each pair, from square to square across their sides, until every pair is joined and every square on the board is used.
Lines never cross and never branch, and each square holds one line. Every puzzle has exactly one answer that fills the board, so when two routes both look possible, the squares left over tell you which.
Rules
- Join each pair of matching numbers with one line that runs through the centres of side-by-side squares, turning only at right angles.
- Lines may not cross, branch or pass through a square twice, and no line runs through a number that isn’t its own.
- Every square must be covered. Joining all the pairs isn’t enough: a board with empty squares left is not solved yet, and the bar above the board says so.
- Drawing over another line cuts it back to where you crossed it. Back up before you let go and the other line grows back; let go and the cut stays.
- A pair whose numbers are joined turns its two numbers solid. The line you are drawing shows in red.
- Each puzzle has exactly one solution, checked by a solver before you see it. Your puzzle stays in this browser, one per size, and the clock only runs while the page is in view.
Controls
- Drag from a number
- Draw a line from it (any line the pair already had is cleared)
- Drag from a line’s loose end
- Carry on drawing it
- Drag back along a line
- Take it back to there
- Tap a line or number
- Clear that pair’s line
- Arrows / WASD
- Move the cursor
- Space / Enter
- Pick up the line at the cursor / put it down
- Arrows while holding
- Draw
- Backspace
- Step back (or clear the line under the cursor)
- Esc
- Drop the line you are holding, undoing that stroke
- Z / Ctrl+Z
- Undo
- P
- Pause
Tips
- Start along the rim and in the corners: a number in a corner has only two ways out, and a line that follows the edge rarely strands a square.
- Look for empty squares with only two open neighbours. A line has to come in one side and leave by the other, so its route through there is already settled.
- Don’t take the short way just because it’s there. Every square has to be filled, so a line that cuts across a gap often leaves a pocket no other pair can reach.
Number Link strategy
Corners and edges first
A number in a corner has two ways out, and one on the edge three. An empty corner square needs a line through it too, and only a line that turns right there can fill it, so ask which pair can reach it. The rim is also where a wrong route shows up soonest, which makes it the best place to start.
Two ways in, one way through
Every empty square ends up in the middle of some line, with one neighbour on each side. A square with only two open neighbours is already settled: the line comes in through one and leaves through the other. If those two neighbours are the loose ends of two different pairs, something earlier is wrong.
No line hugs itself
In the puzzles here no line ever runs alongside itself: two squares of the same line only touch where the line steps from one to the other. So no line makes a tight U-turn or zig-zags to fill a block on its own. If a route you are trying would double back beside itself, some other pair must fill that space.
Every pocket needs a pair
Since every square must be filled, a pocket of empty squares walled off by lines has to be filled by a pair whose two loose ends both open onto it. If no pair can do that, one of the walls is wrong. Check it whenever a long line closes off a corner of the board.
Cutting is free
Drawing across another line cuts it, and backing up before you let go restores it. So try a route by drawing it, see what it leaves, and pull back if it strands a square. Only the clock counts: undos and redraws cost nothing else.
About Number Link
Joining matching pairs with lines is an old puzzle idea: Sam Loyd printed a version in the Brooklyn Daily Eagle in 1897, and Henry Dudeney’s Amusements in Mathematics (1917) has one as “a puzzle for motorists”. The Japanese publisher Nikoli made it a pencil puzzle with strict rules, Numberlink, which first ran in Puzzle Communication Nikoli in 1987. Phone apps such as Flow Free later brought it to touch screens.
Here each puzzle starts as the grid cut into random lines: one-square lines are joined end to end until the board holds the right number of them, and a join is only made if the line never runs alongside itself. The two ends of each line become a pair of numbers, and the puzzle is kept only if a solver finds exactly one way to fill the board.
Questions
Do I have to fill every square?
Yes. In this version, as in the phone apps, every pair must be joined and every square used. Printed Numberlink doesn’t always state that rule, though a well-made puzzle’s answer fills the grid anyway.
Is this Flow Free?
No. Number Link is the pencil puzzle behind apps like Flow Free: the same rules, drawn in ink, with numbers instead of colours. It isn’t made by or connected with the makers of Flow Free.
Does every puzzle have one solution?
Yes. Before you see a puzzle, a solver searches every way of filling the board and keeps the puzzle only if exactly one works.
Which size should I start with?
The 5 × 5, where the Expert level is 0:45. The 7 × 7 comes next at 2:00, and the 9 × 9 at 5:00.
