Bridges — free online hashi puzzle

Every circle is an island, and the number on it says exactly how many bridges must touch it. Bridges run straight up, down, left or right between two islands, never cross each other, and at most two join the same pair. Get every number matched and one more thing has to be true: all the islands must form a single connected group. Nothing may be left as an island cluster of its own.

That last rule is what makes the puzzle more than counting. A layout can satisfy every number and still be wrong because it split the map in two, so the endgame is often about which of two legal-looking bridges keeps everything joined. Every puzzle here is grown from a working network and then checked to have exactly one solution, so it is always finishable by reasoning. Free, no download, and a new map every time you press play.

How to play

• Tap an island, then tap another in the same row or column to build a bridge between them.
• Tapping the same pair again makes it a double bridge; a third tap removes it.
• Bridges cannot cross each other and cannot pass through an island.
• An island turns green when it has exactly the number of bridges it asked for, and red if it has too many.
• The puzzle is done when every island is green and the whole map is joined into one group.
• Use Undo to take back one bridge, or Clear all to start the same map again. Neither costs you anything but time.

Where to start, and the three moves that do most of the work

Start with the islands that have no choice. An island marked 4 with only two directions available must send two bridges each way, and an island marked 6 with three directions must send two in every direction. The general rule: if a number equals twice the number of directions it can reach, every one of those crossings is a double, and you can draw them without thinking any further.

The second move is the near-miss. If an island needs one fewer than the maximum, every direction still gets at least one bridge, because leaving any direction empty would put the rest over the limit. A 3 with two directions available must therefore have a single bridge in each direction at minimum, and one of them becomes a double later. This is where most of the early progress on a hard map comes from.

The third move is the one that catches people out. Two islands marked 1 facing each other can never be joined, and neither can two 2s if a double between them would close them off from everything else: the pair would be a finished map of its own while the rest of the islands are still out there. Whenever you are choosing between two legal bridges, ask which one would strand a group. If you like this kind of deduction, Nonogram and One Line are the closest neighbours here, and Pipes is the other connect-everything puzzle on the site.

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