When playing SlitherLink on moderate or large boards I usually find that after using the basic techniques:

  • filling out the values in the corners
  • setting lines where there are adjacent 3s
  • setting lines where there are 3s diagonally (including cases where they are only separated by 2s)
  • clearing everything around 0s and filling in the lines (if there is only a unique way).

Between them I still only solved like 25% of the board. The rest of the board is usually either empty, or only contain 1s and 2s, from which I cannot really deduce anything. In these cases I usually resort to guessing a line, and trying to trace whether it results in a contradiction eventually, so I can cross it off, but this doesn't seem like an optimal solution.

Are there additional strategies that I can use to continue solving the puzzle?


There are a couple of further strategies. To start, there are a lot more local patterns that allow marking some loop segments and non-loop segments. Bram de Laat wrote up an excellent guide.

Then, there are some global arguments, which hinge on the requirement for a single loop: Some edges may result in a small closed loop, or some edges must be part of the loop in order for the loop to reach some remote area of the grid.

If you bisect the grid along any path, the loop must cross the cut an even number of times. (This is basically the Jordan Curve Theorem.)

Another set of techniques that I don't want to detail here exploit the fact that the puzzle has a unique solution.


There are many more configurations:

  1. If you see a 1 and 3 next to each other on the edge, fill the wall of the 3 on the edge of the puzzle and blank the two sides of the 1 not connected to that.
  2. Just like a 2 on the corner forces the two edges one step away from it to be filled, you can often find 2's in the middle that do the same.
  3. It is very useful to identify what squares are inside the loop-they get divided from the outside ones by the path and often that can show you larger features of the path.

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