Slitherlink スリザーリンク

Slitherlink (スリザーリンク) is a loop puzzle from the Japanese publisher Nikoli. The board is a grid of dots, and some of the square cells between them hold a number from 0 to 3. You connect neighbouring dots with horizontal and vertical lines to make one closed loop. Each number tells you how many of the four sides of its cell the loop uses, while a cell without a number may have any number of sides drawn. The loop never crosses itself, never branches and never touches itself at a dot.

Nikoli calls Slitherlink one of its original puzzles and says its greatest feature is the number of small theorems players discover, all built from four digits and three rules. In Japan fans shorten the name to Sli-Lin. The puzzle also appears in other publications under names such as Fences and Loop the Loop.

LogicPuzzles.io gives everyone the same daily 7×7 Slitherlink each day, plus unlimited 5×5, 7×7 and 10×10 grids. Every puzzle is verified by an exact solver to have exactly one solution, and a second solver that never guesses confirms that it can be finished by deduction alone. Lines, × marks, undo, a timer and a Check button run in your browser, and your progress is saved on this device.

Begin with the numbers that give lines away. A 0 means none of its four sides is used, so mark all of them with ×. A 3 in a corner of the grid always uses both outer sides. When two 3s sit side by side, the side they share and the two sides at either end of the pair are all part of the loop. When a 3 touches a 0, the 3 uses its three sides away from the 0, and the loop continues straight on from the two corners the 3 shares with the 0.

Then work with the dots. Every dot has either no line or exactly two. A dot that already has two lines cannot take a third, so cross out its other sides. A dot with one line and only one side still open must continue through that side, and a dot where every side but one is crossed out cannot be used at all. These two rules extend the loop one segment at a time.

Two ideas carry you through harder spots. First, never close a small loop early: a line that would join the two ends of your path before every number is satisfied must be an ×. Second, think of the loop as a fence with an inside and an outside. Two neighbouring cells on the same side of the fence never have a line between them, and cells on opposite sides always do.

The usual mistakes are treating an empty cell as a 0 and letting the loop touch itself at a dot. Numbers turn grey once satisfied and red when overfilled. The Check button highlights branches and overfilled numbers, and otherwise tells you how many loose ends are left or whether your lines form more than one loop.

Slitherlink is an original Nikoli puzzle. It first appeared in June 1989 in issue 26 of Puzzle Communication Nikoli, where the editor combined two puzzle ideas sent in by readers. In that early form every cell held a number and the lines did not have to form a loop; the single loop and the freedom to leave cells empty came later and gave the puzzle its present shape. Nikoli describes it as a puzzle made with simple rules and just four numbers, 0, 1, 2 and 3, whose appeal lies in the endless supply of small theorems solvers discover, and its Japanese fans call it Sli-Lin. Elsewhere it has been published as Fences, Takegaki and Loop the Loop, and Simon Tatham's free puzzle collection includes a version called Loopy. Computer scientists have shown that solving Slitherlink on grids of arbitrary size is NP-complete.