Build one loop in Slitherlink
Slitherlink combines counts around cells with a single continuous loop. A set of locally correct clues can still fail if it produces a branch, a loose end or two loops.
By Zehano · Original AI-assisted explanation and worked example · Updated 16 October 2026 · Editorial approach
A worked example
Consider a cell marked 3 immediately beside a cell marked 0. The shared edge cannot be drawn because the zero permits no surrounding edges. The other three edges of the 3 must therefore be drawn. That settles a useful local pattern, but it does not settle the entire puzzle. At each corner where a drawn edge ends, inspect which continuation is still possible. An eventual loop uses exactly two edges at each dot it visits. If two edges already meet there, any remaining incident edges must stay unused. Continue these small deductions outward while checking the numbered cells affected by each change.
Try it in three steps
- Read zero clues first and identify their four forbidden edges. Look for neighbouring clues whose remaining possible edges are now exactly the number they require.
- Alternate between cells and dots. Cells constrain the count of surrounding edges; dots constrain how the path can continue without crossing, branching or stopping.
- Before closing a path, inspect the rest of the board. Once a closed loop is formed, no separate drawn segment can join it without breaking the rules. At completion, trace the entire loop back to its starting point.
What to watch for
An empty cell is not a zero clue. It places no direct numerical restriction on its surrounding edges, although the loop rules still apply. Similarly, satisfying every printed number does not excuse disconnected loops or dangling lines.
Apply it to your own material
Choose one topic from your current course or project. Write down the question you want to answer, make an attempt, and keep a note of how you checked it. Use the example above as a pattern; replace its subject matter and assumptions rather than copying an answer into a different task.
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