PlankwayThe only way out: groups that must connect
Where avoid isolation forbids a bridge that would close a group off, this technique forces a bridge that keeps a group connected. Every group must eventually link up with the rest, so if it has only one way out, that way is certain.
The idea
Look at a group of islands that are already linked by certain bridges. List every connection from that group to an island outside it that is still possible. If there is only one, that connection must get at least one bridge, or the group would stay cut off forever.
Why counting alone does not see it
In the example, the 2 in D1 has one bridge and needs one more. Purely by counting, that bridge could go back to the 3 in A1 (as a second bridge) or down to D4. Both look possible. Only when you think about the group as a whole does it become clear that the second bridge to A1 would keep the group closed, and that the bridge must go down.
Once that bridge is in place, the rest follows by counting: D1 is full, so the 3 in A1 takes its last bridge from A4.
Finding these situations
- Look at the edges of the board and at areas surrounded by reefs: groups there have few connections to the outside.
- Think in groups, not islands. Once a few islands are linked, treat them as one big island with its own exits.
- Combine it with crossing bridges: a long certain bridge can cut off exits of a whole region.
In the Plankway solver this technique has weight 4. It is the ceiling for Friday puzzles, and Saturday puzzles are generated so that they need at least this or try and see.