A loop that every dot either visits or skips
Slitherlink is a Japanese loop puzzle played on the lines between dots. The numbers count the sides each square gives the loop, but a quieter rule matters just as much: at every dot, the loop either passes through once or does not touch it at all. That means each dot ends with exactly zero or exactly two lines. Never one, never three.
If a dot already has two lines, cross off its other sides. If it has one line and one free side left, the loop must continue through that side.
Openings that never fail
- Zeros. Mark all four sides of a 0 with ✕. Then look at the dots around it: each has lost one or two of its possible exits, which often forces lines next door.
- Threes in corners. A 3 in a board corner must use both of the corner's outside edges, because the corner dot has only two sides available and the loop cannot stop there.
- Two 3s side by side. The line between them, and the two far sides, are always part of the loop. Draw all three at once.
- Two 3s touching at a corner. The outer corners of the pair are fixed: each 3 uses the two sides that point away from the other.
- A 3 next to a 0. The 0 rules out the shared side, so the 3 takes its other three.
Here is a worked example on the 5×5 Easy board. Say a 3 sits in the middle row with a 0 directly to its right. The 0 crosses off the side they share. The 3 now has exactly three sides left, so all of them are lines: top, left and bottom. Now look at the dot at the 3's top-right corner. Its line arrives from the left, and it cannot go right or down, because both of those are sides of the 0. The only exit is straight up, so draw it. The same reasoning at the bottom-right corner sends the loop straight down. One clue pair gave you five lines.
Working the middle of the board
Once the patterns are in, run three checks over and over.
- Count each square. If a number already has its full count, ✕ the rest of its sides. If it has exactly as many free sides as it still needs, draw them all.
- Check each dot. A dot with two lines is finished. A dot with one line and one free side continues. A dot with no lines and only one free side can never be used, so ✕ that side.
- Check the loop's shape. The loop must be one closed piece. If drawing a side would close a small loop while other lines are still loose elsewhere, that side must be ✕.
The last check unlocks the hardest boards. Late in a puzzle, two loose ends often sit close together. Joining them would close a loop too early, so that gap is ruled out.
Where players go wrong
- Skipping the ✕ marks. A cross is only your note, but on 7×7 and 9×9 boards it is the difference between seeing a forced line and missing it. Mark ruled-out sides as soon as you know them.
- Forgetting blank squares. A square with no number can have any count, but its sides still obey the dot rule. Blank does not mean free.
- Letting branches slip in. A dot where three lines meet turns red. Undo straight away rather than trying to repair it later.
Building up through the levels
Easy is 5×5 with most squares numbered, so the pattern openings usually finish the board. Medium is 7×7 with about seven in ten squares clued, and you will need the dot rule regularly. Hard is 9×9 with only about half the squares numbered, which pushes you onto the loop-shape check.
Try to finish each Easy board using only the openings above and the dot rule. When that feels automatic, move up. On Hard, a hint sets one side for you; when you take one, trace why it had to be that way before you continue. If you enjoy keeping a network in one piece, Hashiwokakero at /games/hashiwokakero works the same muscle with bridges instead of a loop.
