Slitherlink Puzzles
Draw one closed loop along the lines between the dots, so that every number is touched by exactly that many of its four sides. Tap once to draw a line, again to rule it out. Every puzzle here has exactly one loop, and every one can be reasoned out without a single guess.
Also published as loop the loop, fences, and as takegaki by Nikoli, who introduced it in 1989.
What Is Slitherlink?
Slitherlink is played on the lines between dots rather than inside the squares, which is what makes it feel different from every other number grid. You draw a single closed loop that never crosses itself and never branches, and each numbered square tells you exactly how many of its four sides that loop uses. Squares with no number constrain nothing directly. Nikoli published it in 1989 under the name takegaki, and it appears elsewhere as loop the loop and as fences.
The whole puzzle rests on two statements, and it is worth being able to recite both: a number is touched by exactly that many of its sides, and every dot has either no lines or exactly two.
Why Every Dot Has Zero Lines Or Two
This is the rule people underuse, and it does more work than the numbers do. The answer is a loop: a line that arrives at a dot has to leave again. So a dot is either untouched, or the loop passes through it once and uses two of its sides. One line would be a dead end. Three would be a junction. A loop has neither.
Two things fall straight out of it. A dot that already has two lines has all its remaining sides ruled out. And a dot with one line and only one undecided side must use that side — because the alternative is a dead end, and dead ends do not exist. Alternating between the numbers and the dots is what makes a slitherlink move; working only the arithmetic stalls within a few steps.
The Clues That Settle Themselves First
| What you see | What it forces | Why |
|---|---|---|
| Any 0 | All four sides ruled out | It uses none of them, so there is nothing to work out. |
| A 3 in a corner of the field | Its two outer sides drawn | The corner sides cannot both be spared when three are needed. |
| Two 3s side by side | The shared side, and the two outer sides beyond them | Neither 3 can give up the edge between them and still reach three. |
| A 3 diagonally touching another 3 | The two outer sides at each far corner | The loop cannot pass through the shared dot twice. |
| A 1 in a corner of the field | Both corner sides ruled out | Using either would force a dead end at the corner dot. |
Start with the zeros every time. A 0 settles four edges for no effort at all, and each of those edges immediately says something about a dot and about the square on the other side. It is the cheapest move on the board and there is never a reason to leave one unmarked.
Ruling A Line Out Is Half The Puzzle
A slitherlink has three states per edge, not two: undecided, drawn, and definitely not part of the loop. Marking that third state is not bookkeeping — it is how the dot rule becomes usable, because a dot only forces a line once its other sides have been ruled out. Solvers who only draw lines and never cross any out go round in circles on puzzles that are otherwise straightforward. Tapping an edge here cycles through all three.
One Loop, And No Guessing — Both Checked
Two different promises are made about every puzzle on this page, and they are checked separately because they are different things:
- Exactly one loop fits the numbers. Two separate rings can satisfy every clue on the board and still be wrong, so the single-loop condition is verified on its own rather than assumed from the arithmetic.
- No guess is ever needed. A solver that only ever uses the two rules above — never a trial — has to finish the whole grid unaided. If it stalls, the puzzle is thrown away.
Clues are removed one at a time from a fully-numbered grid, and each removal is kept only while both statements still hold. That is why the puzzles carry roughly half the numbers a full grid would: every one that could go, went.
How The Puzzles Are Made
Most loop puzzles are generated by drawing a path and hoping it closes. These are made the other way round. Take any group of squares that is joined up and has no hole in it: the boundary between that group and everything else is a single closed loop, always, with no checking required. The numbers are then read off that boundary. The loop is a consequence of the shape rather than something that has to be repaired, which is why every puzzle here is a genuine loop and none are near-misses.
Slitherlink Puzzles Frequently Asked Questions
What is slitherlink?
A logic puzzle played on the lines between dots rather than inside the squares. You draw a single closed loop that never crosses or branches, and each numbered square says exactly how many of its four sides the loop uses. Also published as loop the loop, fences and takegaki.
What is the best first move in slitherlink?
Cross out all four sides of every 0. It settles four edges at once and costs no thought. After that look at a 3 in a corner, and at any two 3s side by side — both force lines straight away.
Why must every dot have zero or two lines?
Because the answer is a loop. A line that arrives at a dot has to leave again, so a dot is either untouched or passed through once — two sides. One line would be a dead end and three would be a junction; a loop has neither.
Can the loop cross itself or split in two?
No. There is exactly one loop and it never touches itself. Two separate rings can satisfy every number and still be wrong, which is why that condition is checked separately from the clues before a puzzle is ever served.
Do squares without a number matter?
Yes, though not directly. A blank square constrains nothing by itself, but its edges are shared with numbered neighbours and with the dots at its corners, and those settle it in the end.
Does every puzzle here have exactly one answer?
Yes, and it is checked rather than claimed. Every puzzle is verified to have exactly one loop that fits its numbers, and separately verified to be reachable by reasoning alone. A clue is only ever removed while both remain true.
Is it free, and does it need an account?
Completely free, no account, no adverts, nothing uploaded. Your progress stays in your own browser.
What is slitherlink also called?
Fences, Loop the Loop, Loopy, Takegaki, Sli-Lin, Suriza and Dotty Dilemma are all the same puzzle. Nikoli published it in Japan and the English-language names arrived piecemeal as different papers and apps picked it up, which is why a puzzle with one set of rules has collected so many titles.