Slither Link

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Moderately difficult Slither Link puzzle (solution)

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

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

[edit] Rules

Slither Link 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 Slither Link is that every point has either exactly two lines connected to it, or no lines. For example, suppose the lower-right square in a puzzle contains the number 1. Then both line segments which are connected to the lower-right point may be X'ed out, because if they were both lines, then they would exceed the count of 1 for that square.

In a really difficult puzzle, you may be forced to 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.

Another simple helpful strategy 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

Slither Link 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.