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With the listed set of rules, none of the four puzzles are solvable. You need to "upgrade" some of the rules in order to be able to solve them.
Puzzles with red borders are allowed to have triple bridges.
Puzzles with green borders are allowed to have 45-degree diagonal bridges.
Puzzles with blue borders are allowed to have bridges that intersect with each other.
Which bridges used the modified rules? Those bridges will give you the answer.
Connect the circles (“islands”) with straight bridges such that all the circles form one connected component, and
- At most two bridges connect each pair of islands;
- All bridges are horizontal or vertical;
- No two bridges intersect each other.