How to play
Slitherlink is played on a grid of dots. Some squares between the dots hold a number from 0 to 3. Join neighbouring dots with straight lines so that they form one single closed loop. The loop may twist and turn as much as it likes, but it never crosses or touches itself, never branches, and no other lines may be left on the board.
Each number tells you how many of the four sides of its square belong to the loop: a 3 uses three sides, a 0 none. Squares without a number can have any count. Pick a size (5×5, 7×7 or 10×10) and a level, then press Start. The clock stops while you pause or switch to another tab. As soon as your lines form one loop that agrees with every number, the puzzle is solved.
Controls
- Mouse: click an edge between two dots to switch it from empty to line, to a cross and back to empty. A cross is your own note that an edge is not part of the loop. Right-click places or removes a cross directly. Press and drag along the dots to draw several lines at once; dragging back takes the stroke back, and a drag that starts on a line erases.
- Touch: tap and drag the same way; the page does not scroll while your finger is on the board. When the squares are small (10×10 on a phone), a Zoom button appears; while zoomed, move the board with two fingers or pinch.
- Keyboard: the cursor sits on an edge and points at one of its dots. An arrow key walks it from that dot to the next one, like a pen; the first key press only shows the cursor. Space or Enter draws or removes a line, X a cross, Backspace clears, and Shift+arrow draws while moving. Ctrl+Z / Ctrl+Y undo and redo; H hint, C check, P pause, N new puzzle, F full screen.
A number turns grey when it has exactly the right number of lines. A red ring around a number means too many lines; a red ring around a dot means three or four lines meet there, which a single loop never does.
Check shows wrong lines dashed in red and circles wrong crosses until your next move. Hint first removes a wrong mark if you have one. Otherwise it fills in what one number or dot forces by simple counting, or crosses an edge that would close the loop too early, and says why; if nothing is forced, it reveals one edge of the loop.
How it works
An n×n board has (n+1)² dots and 2n(n+1) edges, so the 10×10 board has 121 dots and 220 possible edges. Two facts drive almost every deduction:
A third idea: a closed loop that never touches itself splits the plane into an inside and an outside (the Jordan curve theorem). Colour every square inside or outside, with the area around the grid counting as outside. An edge belongs to the loop exactly when the squares on its two sides have different colours, so a number counts how many neighbours of its square have the opposite colour. Many patterns are this colouring in disguise.
Every puzzle here has exactly one solution. The 1,350 puzzles (150 per size and level) were made by drawing a random loop, noting all its numbers and removing them one at a time while a computer solver could still finish by pure reasoning. Easy needs only counting at numbers and dots plus the rule that the loop must not close early; Medium also needs inside-and-outside reasoning; Hard needs you to test an edge and follow the consequences until something breaks. A second, independent program counted the solutions of every puzzle and found exactly one each time. Each puzzle can also appear rotated or mirrored in eight ways.
Slitherlink first appeared in a Japanese puzzle magazine in June 1989; at first every square held a number and the lines did not have to form a loop. In general, deciding whether a Slitherlink grid has a solution is NP-complete: no fast method is known that works for every possible puzzle.
Tips and strategy
- Start with every 0: cross all four of its sides.
- A 3 in a corner of the grid uses both outer edges at that corner; a 1 in a corner uses neither.
- Two 3s side by side: the edge between them and the two outer edges parallel to it are lines. For two 3s touching diagonally, draw the two outer sides at the far corner of each.
- A line that reaches a dot must go on. When only one way is open, take it; when two lines already meet at a dot, cross the rest.
- Never close a small loop while other lines or numbers still need it.
Frequently asked questions
Why is the 10×10 board small on my phone?
Eleven dots across a phone screen leave about 33 pixels per square. Use the Zoom button or pinch with two fingers, or play 5×5 and 7×7, which fit with large squares.
Sources
- Yato T (2000). On the NP-completeness of the Slither Link puzzle. IPSJ SIG Technical Report 2000-AL-74, 25–31. The proof that deciding whether a puzzle has any solution is NP-complete.
- Wikipedia contributors (accessed 25 October 2026). Slitherlink. Wikipedia. Encyclopedia article. The first publication in June 1989 and the early rules without a loop.