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This island's number equals everything its remaining connections could possibly carry — every one of them must be filled to its maximum.

Bridge to add
Islands that establish the pattern

How it works

The corner island needs 4 bridges, and it only has two possible directions — right and down.
Each direction can carry at most 2 bridges, so 2 + 2 is exactly 4: there's no slack at all.
Both connections must be double bridges. The same logic applies to a 6 on an edge or an 8 anywhere.