A lane is a straight path between two visible islands, and it can hold one or two bridges. Subtract bridges already placed, fill forced lanes, and keep every island in one connected group.
First subtract any bridges already placed. If an island can reach only one neighbor, put every bridge it still needs in that lane.
Before: two 1-islands sit on the top row, each with a single visible neighbor.
After: each top 1 has its only bridge. The lower island numbered 2 still needs two bridges and has only one lane. Its double bridge is the next move.
Count what each lane must carry
Place the certain singlesIf an island needs three bridges across two open lanes, each lane must get at least one bridge. You can decide which one is double later.Close a finished islandOnce an island has its full number, rule out every unused lane from it. Its neighbors may then have fewer choices.Recount after a crossingA bridge blocks every lane that would cross it. Recheck the islands at both ends of each blocked lane.Protect the last exitIf a group of joined islands has only one lane left to the rest of the board, that lane must be used.
Do not choose the double too early
A 3 with two open lanes needs one bridge in each lane, but either lane might later take the second bridge. Place the two certain singles first and wait for another clue to choose the double.