Loop-The-Loop

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.

Related puzzles:

Bridges, Futoshiki, Hitori, Inside And Outside The Loop, Isolate, Loopy, Masyu, Numberlink, Nurikabe, Yajilin
The illustration of the puzzle Download example puzzle

Instructions:

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.

Download further details Interactive tutorial

Featured in:

  • Sudoku

Also appears in:

Beyond Sudoku, Kakuro, Saga Magazine Puzzles