Single loop
All lines form one closed loop.
Logic / 4 modes
Loops
All lines form one closed loop.
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One game. Several approaches.
Two loops
Exactly two independent closed loops are required.
Hex loops
Build one loop on a genuine hex-cell graph. Each number counts the cell boundary edges in the loop. Every used vertex has degree two. Blue fixed edges participate in independent uniqueness checking.
Loop zones
One loop on a square lattice. Alongside edge counts, I must be inside and O outside. Zones are determined by reachability from the exterior through non-loop edges. Blue fixed edges cannot be changed.