Plankway

Every bridge counts: islands that need all they can get

The opposite of a full island: an island whose number is so high that it needs every bridge it could possibly get. Then there is no choice left, and you can build all of them at once.

Count the maximum

For each neighbour an island can see, the maximum is two bridges, or less if that neighbour has less room. Add those maximums up. If the total equals the island’s number, every one of those bridges is certain.

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A 4 with two neighbours: 2 + 2 = 4, so both connections are double bridges.

The well-known cases: a 4 with two neighbours, a 6 with three, and an 8 with four. An 8 is rare, but when you see one, all eight bridges around it are certain straight away.

Reefs make it happen more often

A reef can hide a neighbour. In the figure, the 6 in C3 seems to have four neighbours, but the reef in C4 blocks the way to the 1 below. With three neighbours left, 2 + 2 + 2 = 6, so all three connections become double bridges.

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The reef in C4 blocks one neighbour. The 6 needs a double bridge to each of the other three.

More about this in the article on reefs.

Less room means a lower maximum

The maximum is not always two. A neighbour with a 1 can only ever give one bridge, and a neighbour that is already half full may have room for just one more. Always count what a neighbour can still take, not just what the connection allows.

That makes this technique stronger as the puzzle fills up: the more is known, the lower the maximums, and the more islands suddenly need everything they can still get. If the total is not quite enough to fix every bridge, look at at least one instead.

Recent puzzles that needed this technique

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