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Clues and Strategies:

First step: things to look for to start solving the puzzle

Islands: using the Pigeon Hole Theorem, we can determine some line segments (note that the outcome listed here only guarantees certain lines but IS NOT final)

Number on an Island Number of Possible Destinations Results
8 4
7 4
6 3
5 3
4 2
3 2
2 1
1 1

Doing this process repeatedly throughout the puzzle should be enough to solve it.

Each connected bridge benefits tremendously because it rules out many possibilities. For example:

  • if a "4" has 3 islands it can link to, given that one and only one bridge is established with one of the islands, the condition would be equivalent to a "3" with 2 possible islands.
  • if a "6" has 4 islands it can link to, but one one of them is blocked by a bridge, it would be equivalent to a "6" with 3 islands.

Finally, two unconnected sets of islands should not be created, as in the "solution" below:

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