Also known as:
Dotty Dilemma, Fences, Ouroboros, Sli-Lin, Slitherlink, Suriza, Surizarinku, Takegaki
This puzzles can be described as a regular lattice of dots, with numbers inside some of the squares formed by the dots. The objective is to connect the dots with horizontal and vertical lines to form a single unbroken loop. The number inside a square indicates how many of its four sides form segments of the loop. At no point will the loop cross itself. The path of the loop can be determined by a process of logic, it is never necessary to guess.
The puzzle is probably derived from an earlier two-player pencil game played on a grid, in which turns are taken to link gridline segments without closing the loop, or crossing, or creating a separate branch – until one player (the loser) is forced to do just this.
Loop-the-Loop was first published under the name Slitherlink in the June 1989 edition of Nikoli's 'Puzzle Times'.
A few hints can be offered:
Mark places where you know the loop will not go with an x.
The common edge between horizontally or vertically adjacent 3s must always be a segment, or a closed loop would be formed.
If a 3 lies adjacent to a 0, all three edges of the 3 can be drawn in immediately.
Every dot has either two segments connected to it, or no segments. This means that, for example, if a 3 is in one of the outer corners of the grid, the outside edges of the corner can be drawn in.
Wherever a corner in the loop is formed, no other lines can join at that point, so dots leading to that corner can be marked with a x.
There are other solving strategies, but it is easier to solve the puzzle and discover them for yourself, than to try to understand a dry explanation of them.
Connect adjacent dots with vertical or horizontal lines so that a single loop is formed with no crossings or branches. Each number indicates the number of lines that surround it, while empty cells may be surrounded by any number of lines.
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