How to play Ursa Bridges

In Ursa Bridges, your goal is to connect all the islands with bridges, so that each island has as many bridges as its number says. In the end, they all form a single network.

The rules

Each island has exactly the number of bridges it shows.
Bridges run in straight lines, horizontally or vertically, and only connect neighbouring islands: the next island in the same row or column.
Two islands can be connected by at most two bridges.
Bridges cannot cross each other or pass over other islands.
In the end, all the islands must be connected in a single network.
Every puzzle has exactly one solution, which can always be found by logic alone, without guessing.

Placing and removing bridges

Drag from an island towards its neighbour: the first time places a bridge, the second makes it double, and the third removes both. You can also tap the water between the two islands.

On a computer, hovering over an island shows the connections it can still take, and right-clicking the water removes the bridges on that connection. A connection that would cross a bridge already in place won't take any bridges. When an island has all its bridges, it lights up blue.

How to solve it

Start with the islands that leave you the fewest choices: those with few neighbours and those with high numbers.

A complete island takes no more bridges.
A 1 never has a double bridge, and two 1s are never connected to each other: they would be complete and cut off from the rest.
A bridge in place blocks every connection that crosses it.

All that fit: when an island needs every bridge it still has room for, place them all. A 2 with only one neighbour gets a double bridge; a 4 in a corner, two each way; an 8, two to each of its four neighbours.

The highlighted 2 has only one neighbour, the 4 to its right. Both of its bridges go there: a double bridge.

At least one: if an island would still be short of bridges even with the maximum on its other connections, the remaining connection has at least one. A 3 with two neighbours has at least one bridge on each side; so does a 5 with three neighbours.

The highlighted 3 has only two neighbours. Even with a double bridge to one of them, it still needs one more: there is at least one bridge on each side.

No isolated groups: if some bridges would leave a group of islands complete and cut off from the rest, those bridges cannot be there. That is why two neighbouring 2s never have a double bridge between them.

A double bridge between the two highlighted 2s would complete them both and cut them off from the rest. There can be at most one bridge between them.

The only way out: when a group of islands has only one possible connection to the rest of the network, that connection has at least one bridge.

The six highlighted islands have only one way out to the rest of the network: their other connections are blocked by bridges already in place, or have no neighbour. Without the green bridge they would be cut off, so it has at least one.

The Hint

The Hint button doesn't give away the solution all at once: it first shows you where to look, and only then which bridges are decided. It uses these techniques, starting with the simplest and moving on to the more advanced, so it also teaches you how to solve. It counts as help: a puzzle solved with a hint doesn't count towards your best time or the comparisons with other players.