Slitherlink Puzzle

Slitherlink, generated with a guaranteed single answer

The rules fit in a sentence. Draw one loop along the grid lines, closed, never crossing or branching, arranged so that every numbered cell finishes with exactly that many of its four sides used.

From that, a surprising amount of deduction follows. A 0 kills four edges at once. A 3 in a corner is almost fully determined before you have drawn anything. Two diagonally touching 3s force the edges between them. None of that is stated on the sheet, and working it out is the pleasure of the puzzle.

Grid size and how many to a page

Three sizes: 6×6, 8×8 and 10×10. Six is a five-minute puzzle. Ten, with the clue count deliberately kept near half, will hold a competent solver for a good while.

Puzzles per page runs from 1 to 4. At four, a 10×10 grid is printed small enough that you will want a sharp pencil; at one, it fills the sheet.

Uniqueness is checked, not assumed

This matters more in Slitherlink than in most puzzles, because a loop puzzle with two valid answers gives no warning — you simply finish, and you are wrong, or you are right, and there is no way to tell which.

So the generator builds a random loop, computes the clue for every cell, and confirms the full clue set admits exactly one solution before it removes anything. It then takes clues away one at a time, re-solving after each removal and putting the clue back if a second solution appears. It aims for roughly half the cells revealed and stops short of that whenever going further would make the puzzle ambiguous. If the carving cannot get anywhere without breaking uniqueness, it prints the full clue set, which is easier but never wrong.

The consequence: some sheets carry more numbers than others. That is the uniqueness guarantee showing through, not an inconsistency.

Solutions

The solutions toggle adds a page with the loop drawn in for every puzzle on the sheet. Off for a puzzle book. On for a class, where twenty attempts need checking in the time it takes to walk round the room.

Starting techniques worth teaching

A 0 means all four of its sides are out. Cross them first. It opens the board faster than anything else and it is the move beginners skip.

After that, look at 3s next to 0s, at 1s in corners, and at any cell where three sides have already been decided. Slitherlink rewards working the constraints rather than guessing a route, and a solver who guesses will get a plausible-looking loop that fails one clue somewhere on the far side of the grid.

Also called

Loop the Loop, Fences, Takegaki, Number Line. It comes from the Japanese puzzle publisher Nikoli, same house as Sudoku, and it remains far less common in Western puzzle books than it deserves — which is the main reason for generating your own.

Print at 100% on A4 or US Letter. Every generation is new; the seed reproduces a set exactly if you want the same puzzles twice.