Two bridges
Connect all islands in one network, at most two bridges per edge.
Logic / 3 modes
Bridges
Connect all islands in one network, at most two bridges per edge.
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One game. Several approaches.
Three bridges
Allow up to three parallel bridges between neighboring islands.
Diagonal bridges
Connect nearest islands horizontally, vertically or along 45° diagonals. Each pair holds 0–2 bridges. No crossing; satisfy all degrees and form one network. Generation checks uniqueness, with a simple chain fallback after bounded attempts.