Draw bridges only horizontally or vertically between two islands that are the nearest islands visible to one another in that direction. A bridge must begin and end at islands; it may not pass through an island.
Connect a pair of islands with at most two bridges. A single bridge counts as 1 at each endpoint and a double bridge counts as 2.
The total number of bridge lines touching an island must equal the number printed on that island.
Bridges may not cross one another. All islands must be connected, directly or through other islands, in one network.
The puzzle is solved only when every island has its exact total, no bridges cross or pass through islands, and the complete network is connected. Every published Bridges puzzle has exactly one valid solution.
An island numbered 1 can take only a single bridge, so it can never be joined to a neighbour by a double. An island numbered 2 with only one visible neighbour must take a double to that neighbour.
Example: A 2 sits in a corner with just one island in line with it. Draw a double bridge between them straight away.
Count an island’s visible neighbours and multiply by two — that is the most it could ever hold. When its number equals that maximum, every one of those corridors carries a double.
Example: A 6 has exactly three visible neighbours. All three corridors are doubles, because 3 × 2 = 6.
When an island’s number is one less than its maximum, every corridor must carry at least a single: leaving any of them empty would put the target out of reach.
Example: A 7 with four neighbours can spare only one line, so all four corridors take at least one bridge. Draw the singles now and decide the doubles later.
Subtract what an island already has from its number, then add up what its still-usable corridors could still carry. If the two are equal, every one of those corridors goes to its maximum.
Example: A 5 already has two bridges and has three corridors that could each take one more. All three take that extra bridge.
Two corridors that would cross cannot both carry a bridge. The moment one of them is certain, the other is empty for good — which often starves an island of options and decides its bridges instead.
Example: A long horizontal corridor is confirmed. Every vertical corridor it passes over is dead, so the islands at their ends must find their bridges elsewhere.
A bridge that would complete a small group of islands whose numbers are all satisfied, while other islands sit outside it, is illegal — the finished network has to be one piece.
Example: Two 1s facing each other would satisfy both at once and seal them off from the rest of the board. That bridge cannot be right unless those two are the only islands.
Every bridge counts once at each end, so the sum of all the island numbers is always twice the number of bridge lines. It is a quick way to sanity-check a board that feels wrong.
Example: The islands add up to 40, so a finished board holds exactly 20 bridge lines.
A noted bridge is a real bridge — it counts towards every island’s total exactly as a plain one does — but it is drawn in red, so you can see at a glance which parts of the network you were guessing at and which you had proved.
Example: Shift-click the water between two islands to place that bridge as a note; once a neighbouring island settles it, press it again as a plain bridge.