LOGIC PUZZLE
Numberlink online free
Connect the pairs of dots of the same colour. Paths cannot cross, and in the end they must fill every square. Each grid has exactly one solution: it is not a random grid hoped to be solvable, it is built the other way round.
Drag from a coloured dot to its twin. Entering a path you already drew cuts it from there on, so you can redo a stretch without clearing everything. Starting again from a tip redraws that connection from scratch.
How to play
The grid holds pairs of dots of the same colour. You have to join every pair with a path that moves horizontally and vertically, never diagonally.
Two rules, and they are what make this a logic problem rather than a pastime: paths may not cross or overlap, and when you are done no square may be left empty. The second rule is what decides everything: without it there would be endless solutions.
Three things to look at
The corners
A corner square has only two neighbours. If a path runs through it, that path enters by one and leaves by the other: there is no alternative. Corners and edges are always the place to start from.
The corridors
When a run of free squares is one wide, whichever path enters it must run the whole length. Spotting corridors before drawing saves you from discovering halfway through that you have shut yourself out.
The squares left over
Because every square must be covered, a free square surrounded by other people's paths is a mistake already made: somebody will have to pass through, and if nobody can, the routing has to be redone. Counting the squares left matters as much as looking at the dots.
The options
- Size — 5×5, 6×6 or 7×7, from five to ten pairs of dots.
- Hints — complete one open connection, copying it from the solution.
- Clear — wipes every path and leaves the dots where they are.
- Resume — the game saves itself: close the tab and find it where you left it.
Frequently asked questions
Are Numberlink and Flow the same game?
Yes, the rules are the same. «Numberlink» is the name of the puzzle as it appeared in Japanese magazines, «Flow» the name of the app that made it popular. In Japan it also goes by «Arukone».
Is it free?
Yes, it plays free in your browser. No sign-up, no account, no advertising and no data collection: the whole game runs on your device.
Do I have to fill every square?
Yes, and that is the rule that makes the puzzle interesting. If connecting the pairs were enough there would be a great many solutions; requiring every square to be covered is what leaves exactly one.
Do the grids really have a single solution?
Yes. Every grid goes through a solver that counts solutions and stops as soon as it finds two: if more than one exists the grid is discarded and another is generated.
Does it work on a phone?
Yes, and that is the best way to play: you draw with your finger starting from a coloured dot. The buttons at the bottom adjust the zoom and fit the grid to the screen.
Is progress saved?
Yes. The game in progress is kept in your browser's local storage, so you can close the tab and pick up where you left off. The save never leaves your device.
How it is built
Kakuro, which I tried before this one, ran aground on exactly this point: filling a grid at random and hoping it has a single solution almost never works. Numberlink lets you flip the problem around.
The generator does not place the dots and then look for paths. It does the opposite: it grows random paths until they have covered every square, and only then takes the two ends of each and calls them a pair of dots. A solution therefore exists by construction — it is the very one it just drew.
What remains is checking that it is the only one, and that is the solver's job: it explores the possible routings with two prunings, that every open pair can still reach its twin through free squares, and that no free square ends up cut off from everything. It stops the moment it finds a second solution, because at that point the grid is already fit for the bin.
Measured: of the random partitions, only 14-20% have a single solution. Everything else is discarded before you ever see it.
It comes out of the same way of working I apply to products: Miraviso is a real case, and if you need a hand with something similar, start here.