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Asked
Modified 7 months ago
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In the following partially filled Slitherlink, what would be a logical next step that does not rely much on guess-and-backtrack?

screenshot of partially filled Slitherlink

Rules for Slitherlink:

  • Make one single connected loop over the edges of the grid
  • The number in each square denotes how many edges on that square are part of the loop
  • Empty square means it can have any number of edges

Note: This is from a Slitherlink puzzle app I usually use, and normally I could finish small grid like this in about 1 minute. But this particular one stumped me for a while, so I present it here to find other logical patterns that I might have not known about.

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1 Answer 1

16
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A common technique is to divide the playing area into two parts, and then use the fact that the closed slitherlink loop must cross the border between those two areas an even number of times.

In this case:

Cut off top right corner area
The area around the top right corner can be cut off, shown with a red line in the left picture. This line crosses two filled in edges, two open edges of the middle 2 clue for which we know exactly one will be filled in, and one other open edge. That's a total of 3 known filled edges, so to make this even we need one more. That can only be the other open edge, which is filled in in the picture on the right.

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2
  • $\begingroup$ Ah, yep, I was using this loop trick as well, but since there are much more possibilities with this trick, I missed this one. Good find! (how did you draw the edge btw, lol). And yep, this single edge finishes the puzzle quite easily. 🎉 $\endgroup$
    justhalf
    –  justhalf
    2025-02-25 12:50:03 +00:00
    Commented Feb 25 at 12:50
  • 4
    $\begingroup$ @justhalf I just used MSPaint, and copied the existing edge. $\endgroup$
    Jaap Scherphuis
    –  Jaap Scherphuis
    2025-02-25 13:08:36 +00:00
    Commented Feb 25 at 13:08

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