Slitherlink

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Moderately difficult Slitherlink puzzle (solution)

Slitherlink (also known as Fences, Loop the Loop, Ouroboros and Dotty Dilemma) is a logic puzzle published by Nikoli. As of 2005, 17 books consisting entirely of Slitherlink puzzles have been published by Nikoli.

1 Rules
2 Solution Methods
3 History
4 See also
5 External links

[edit] Rules

Slitherlink is played on a rectangular lattice of dots. Some of the squares formed by the dots have numbers inside them. The objective is to connect horizontally and vertically adjacent dots so that the lines form a single loop with no loose ends. In addition, the number inside a square represents how many of its four sides are segments in the loop.

[edit] Solution Methods

Whenever the number of lines around a cell matches the number in the cell, the other potential lines can be eliminated. This is usually done with an X.

A key to many deductions in Slitherlink is that every point has either exactly two lines connected to it, or no lines. For example:

If a 1 is in a corner, the actual corner's lines may be X'ed out, because a line that entered said corner could not leave it except by passing by the 1 again. This also applies if two lines leading into the 1-box at the same corner are X'ed out.
If two 3s are adjacent to each other horizontally or vertically, their common edge must be filled in, because the only other option is a closed oval that is impossible to connect to any other line. Also, the two outer lines of the group (parallel to the common line) must be filled in.
If two 3s are adjacent diagonally, the edges which do not run into the common point must be filled in.
If the line reaches a corner of a 3, there must be lines on both sides of the 3 that said corner is not adjacent to, because if the 3's sole empty space were not adjacent to it, the corner would have three lines connected to it.

In an exceptionally difficult puzzle, one may use another mathematical theorem, which states that any open curve that starts and ends outside of a closed curve must intersect the closed curve an even number of times. In particular, this means that any row of vertical lines or any column of horizontal lines must have an even number of lines. When only one potential line segment in one of these groups is unknown, you can determine whether it is part of the loop or not with this theorem.

A simple strategy to assist in using this theorem is to "paint" (sometimes called "shade") the outside and the inside areas. When you see two outside cells, or two inside cells be next to each other then you know that there is not a line between them.

[edit] History

Slitherlink is an original puzzle of Nikoli; it first appeared in Puzzle Communication Nikoli #26 (June 1989). The editor combined two original puzzles contributed there, and it was completed. At first, every square contained a number.