The full logical solve of the hard Slitherlink for September 8 to September 14, 2026, 12 × 12. 233 steps, 12 techniques, no guessing. Step through it, or jump to any step below.
The 0 at row 6, column 7 uses none of its four sides. Cross every one.
The 0 at row 7, column 5 uses none of its four sides. Cross every one.
The 0 at row 8, column 6 uses none of its four sides. Cross every one.
The 0 at row 11, column 8 uses none of its four sides. Cross every one.
The 0 at row 12, column 3 uses none of its four sides. Cross every one.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
The 3 at row 7, column 4 has exactly three sides that can still be lines. It needs all of them.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 3 at row 8, column 4 has exactly three sides that can still be lines. It needs all of them.
The 1 at row 9, column 4 already has one line. Its other sides are ×.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 1 at row 9, column 3 already has one line. Its other sides are ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
The 3 at row 12, column 8 has exactly three sides that can still be lines. It needs all of them.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The corner dot has no other sides, so the 3 at row 1, column 1 uses both sides there or neither. A 3 can’t skip two sides, so both are lines.
The corner dot has no other sides, so the 3 at row 1, column 12 uses both sides there or neither. A 3 can’t skip two sides, so both are lines.
Every other side at that corner dot is ×, so the 1 at row 5, column 6 uses both sides there or neither. Both would be two lines, so both are ×.
Every other side at that corner dot is ×, so the 1 at row 7, column 7 uses both sides there or neither. Both would be two lines, so both are ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
The 1 at row 7, column 7 has exactly one side that can still be a line. It needs it.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 2 at row 8, column 7 has exactly two sides that can still be lines. It needs all of them.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
Every other side at that corner dot is ×, so the 1 at row 5, column 5 uses both sides there or neither. Both would be two lines, so both are ×.
The 1 at row 5, column 6 has exactly one side that can still be a line. It needs it.
Every other side at that corner dot is ×, so the 1 at row 10, column 5 uses both sides there or neither. Both would be two lines, so both are ×.
The 1 at row 10, column 4 has exactly one side that can still be a line. It needs it.
Every other side at that corner dot is ×, so the 1 at row 11, column 2 uses both sides there or neither. Both would be two lines, so both are ×.
Every other side at that corner dot is ×, so the 1 at row 12, column 10 uses both sides there or neither. Both would be two lines, so both are ×.
The 3s at row 1, column 1 and row 2, column 2 touch at a corner. The two sides of each that face away from the other are lines.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line runs into a corner of the 3 at row 11, column 5 from outside. That dot can take one more line, so the 3 can’t use both sides there. It uses the two sides away from that corner.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
Suppose this side were ×. Following the counting rules from there, some dot or number breaks. So it’s a line.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Suppose this side were ×. Following the counting rules from there, some dot or number breaks. So it’s a line.
Suppose this side were ×. Following the counting rules from there, some dot or number breaks. So it’s a line.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Suppose this side were ×. Following the counting rules from there, some dot or number breaks. So it’s a line.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
The 1 at row 10, column 5 has exactly one side that can still be a line. It needs it.
The 3 at row 11, column 5 already has three lines. Its other sides are ×.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
Suppose this side were ×. Following the counting rules from there, some dot or number breaks. So it’s a line.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
Suppose this side were ×. Following the counting rules from there, some dot or number breaks. So it’s a line.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 1 at row 10, column 8 already has one line. Its other sides are ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
The 2 at row 10, column 9 has exactly two sides that can still be lines. It needs all of them.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
Suppose this side were ×. Following the counting rules from there, some dot or number breaks. So it’s a line.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 2 at row 11, column 10 already has two lines. Its other sides are ×.
The 1 at row 12, column 10 already has one line. Its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
The 3 at row 11, column 11 has exactly three sides that can still be lines. It needs all of them.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
Suppose this side were ×. Following the counting rules from there, some dot or number breaks. So it’s a line.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 1 at row 11, column 2 already has one line. Its other sides are ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
The 2 at row 10, column 2 has exactly two sides that can still be lines. It needs all of them.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Try the highlighted side both ways. Whether it is a line or ×, the counting rules force the same marks, so those marks are certain.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Try the highlighted side both ways. Whether it is a line or ×, the counting rules force the same marks, so those marks are certain.
Try the highlighted side both ways. Whether it is a line or ×, the counting rules force the same marks, so those marks are certain.
Every other side at that corner dot is ×, so the 1 at row 1, column 8 uses both sides there or neither. Both would be two lines, so both are ×.
Suppose this side were ×. Following the counting rules from there, some dot or number breaks. So it’s a line.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Suppose this side were ×. Following the counting rules from there, some dot or number breaks. So it’s a line.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Suppose this side were ×. Following the counting rules from there, some dot or number breaks. So it’s a line.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line runs into a corner of the 3 at row 4, column 8 from outside. That dot can take one more line, so the 3 can’t use both sides there. It uses the two sides away from that corner.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
Suppose this side were ×. Following the counting rules from there, some dot or number breaks. So it’s a line.
The 2 at row 3, column 8 already has two lines. Its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
The 1 at row 1, column 8 has exactly one side that can still be a line. It needs it.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
Suppose this side were ×. Following the counting rules from there, some dot or number breaks. So it’s a line.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Suppose this side were ×. Following the counting rules from there, some dot or number breaks. So it’s a line.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Suppose this side were a line. Following the counting rules from there, some dot or number breaks. So it’s ×.
Try the highlighted side both ways. Whether it is a line or ×, the counting rules force the same marks, so those marks are certain.
Try the highlighted side both ways. Whether it is a line or ×, the counting rules force the same marks, so those marks are certain.
Suppose this side were ×. Following the counting rules from there, some dot or number breaks. So it’s a line.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 2 at row 1, column 3 already has two lines. Its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
Suppose this side were ×. Following the counting rules from there, some dot or number breaks. So it’s a line.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 2 at row 4, column 3 already has two lines. Its other sides are ×.
The 2 at row 5, column 3 has exactly two sides that can still be lines. It needs all of them.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
The 1 at row 5, column 5 has exactly one side that can still be a line. It needs it.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
The 2 at row 4, column 4 has exactly two sides that can still be lines. It needs all of them.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 2 at row 3, column 4 already has two lines. Its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
The 1 at row 5, column 9 has exactly one side that can still be a line. It needs it.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 1 at row 4, column 11 already has one line. Its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 3 at row 3, column 12 already has three lines. Its other sides are ×.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 1 at row 5, column 11 already has one line. Its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 3 at row 1, column 12 has exactly three sides that can still be lines. It needs all of them.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 3 at row 2, column 10 has exactly three sides that can still be lines. It needs all of them.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
Drawing this side would close a loop and leave other lines outside it. There is only one loop, so it’s ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 1 at row 6, column 9 already has one line. Its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
Drawing this side would close a loop and leave other lines outside it. There is only one loop, so it’s ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 2 at row 7, column 9 already has two lines. Its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
Drawing this side would close a loop and leave other lines outside it. There is only one loop, so it’s ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 1 at row 8, column 1 already has one line. Its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
This dot has no line and only one open side. A line there would stop dead at the dot, so it’s ×.
Suppose this side were ×. Following the counting rules from there, some dot or number breaks. So it’s a line.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 1 at row 7, column 11 already has one line. Its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
Drawing this side would close a loop and leave other lines outside it. There is only one loop, so it’s ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
This dot already has two lines. The loop can’t branch, so its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
Drawing this side would close the loop while the 2 at row 9, column 11 still has the wrong count. So it’s ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
The 2 at row 9, column 11 already has two lines. Its other sides are ×.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.
A line ends at this dot, and only one side is still open. The loop can’t stop here, so it goes on that way.