Slitherlink

Slitherlink (also known as Fences, Takegaki, Loop the Loop, Loopy, Ouroboros, Suriza, Dotty Dilemma, and Sli-Lin) is a type of path-drawing logic puzzle designed and published by Nikoli. The premise involves drawing a loop on a lattice that satisfies the border requirements set out by the numbered spaces.

Background

Slitherlink as a genre was first published in June 1989 in Puzzle Communication Nikoli issue 26. The ruleset for the genre was suggested by 矢田レーニン ("Yada Renin"). Determining whether a general slitherlink puzzle is solvable was shown to be NP-complete by Takayuki Yato in 2000.

TO DO

Puzzle Application

An unsolved Slitherlink puzzle

Most slitherlinks are presented in a rectangular lattice grid as shown, with some of the squares having a number. These numbers, which range from 0 to 3, indicate how many of its borders are part of the loop.

The primary method of changing the way the puzzle is solved is by changing the shape or size of the grid, as any planar graph can be used in place of a simple rectangular grid. In fact, the only non-rectangular lattice formed by regular polygons are triangular lattices or hexagonal lattices.

Strategy

Solution to the above Slitherlink example.

Many of the strategies not only involve drawing lines that would go on the loop but marking line segments that would not go on the loop. Below are some examples.

• Squares containing a 0 can immediately have all of its sides be marked as not on the loop.
• Squares containing a number N that have 4-N of its sides be marked as not on the loop have the rest of the sides on the loop.
• Squares on the corner containing a 3 must have the two sides touching the edge of the grid be part of the loop.
• Two adjacent squares each containing a 3 must have the segment between them be part of the loop.
• Because the loop can not self-intersect, each lattice point can have 0 or 2 segments (either a line or a turn) coming from that point. This can eliminate some segments or force the line to go a certain way.
• Segments that reach a "dead end" can also be marked as not on the grid.

Notable Examples

Played Straight

• Magic Mushrooms (MIT Mystery Hunt 2014) (web) - Some of the numbers in this slitherlink are marked by a mushroom to indicate that they are off-by-one.
• Join, Or Die (Shardhunt 2023) (web) - This slitherlink uses a triangular grid but otherwise works normally.

Notable Twists

• Cubism (MIT Mystery Hunt 2016) (web) - This is a 3D version of slitherlink, in which the goal is to create a 2D surface.
• Good Fences Make Sad and Disgusted Neighbors (MIT Mystery Hunt 2018) (web) - This slitherlink uses a hexagonal grid, but only some of the numbers actually represent slitherlink rules.
• Slitheɹlᴉuʞs (MIT Mystery Hunt 2021) (web) - These slitherlinks are not only combined with other logic rules but also involve a literal twist on the paper.

See Also

• Puzzles that involve Slitherlinks
• Slitherlink Puzzles on puzz.link