11 Patterns for the Loop Puzzle (Slitherlink)
In the Loop Puzzle (same rules as Slitherlink), a shape that decides a line or a cross the moment you spot it is called a "pattern". Here 11 patterns are explained on real boards from Puzzle Lounge's free puzzles. The rules and how to count the numbers are in How to play, and one puzzle solved from start to finish with patterns is in Solving one 8×8 puzzle.
List of patterns
In the pictures, violet lines are drawn lines, and a grey × marks a side with no line. Rows count from the top and columns from the left. The number on the right is how many of the 120 free puzzles, worked through by counting and patterns, had a moment when that pattern decided a line or cross that counting alone could not.
| If you see this shape | Patterns | Puzzles it appears in |
|---|---|---|
| A 3 in a corner square of the board | 1. A 3 in a corner | 48 puzzles |
| A 1 in a corner square of the board | 2. A 1 in a corner | 34 puzzles |
| A 2 in a corner square of the board | 3. A 2 in a corner | 19 puzzles |
| 3s across or down, 2 in a row | 4. 3 and 3 side by side | 103 puzzles |
| 3s touching diagonally, 2 of them | 5. 3 and 3 corner to corner | 93 puzzles |
| 0 next to 3 | 6. A 3 next to a 0 | 17 puzzles |
| The 2 sides leading out of a 3's corner dot are both crossed | 7. A 3's corner closed in by crosses | 102 puzzles |
| 1 line comes from outside to a 3's corner dot | 8. A line into a 3's corner | 85 puzzles |
| The 2 sides leading out of a 1's corner dot are both crossed | 9. A 1's corner closed in by crosses | 87 puzzles |
| 1 line comes from outside to a 1's corner dot | 10. A line into a 1's corner | 97 puzzles |
| On one diagonal, 2s run between 3 and 3 | 11. 3 and 3 on a diagonal with 2s between | 38 puzzles |
1A 3 in a corner
A 3 in a corner of the board always has lines on the 2 sides at the corner. A dot in a corner of the board has only 2 sides, so those 2 sides are both lines or both crossed. If both were crossed, only 2 sides would be left, too few for a 3.
See the whole board
The bottom left corner of Easy No.4: the 3 at row 6, column 1. Even on a board with nothing drawn yet, you can draw lines on its bottom and left sides.
2A 1 in a corner
A 1 in a corner of the board has the 2 sides at the corner crossed. A dot in a corner of the board has only 2 sides, so those 2 sides are both lines or both crossed. If both were lines, that would be 2 lines, more than 1, so both are crossed.
See the whole board
The top right corner of Easy No.10: the 1 at row 1, column 6. Cross its top and right sides.
3A 2 in a corner
The squares next to a 2 in a corner of the board have lines on their edge sides. If the 2 corner sides are lines, that uses up the 2, and the line can only go on along the edge. If the 2 corner sides are crossed, the 2's 2 inner sides are lines, and they too can only go on along the edge. Either way, the neighbouring edge sides are lines.
See the whole board
The bottom left corner of Easy No.30: the 2 at row 6, column 1. The bottom side of row 6, column 2 (its right neighbour) and the left side of row 5, column 1 (the neighbour above) are lines.
43 and 3 side by side
With 3 and 3 side by side, across or down, the side between them and the two outer sides, 3 in all, are lines. With no line on the middle side, the other 6 sides would form 1 small loop around the 2 squares and close it. The outer sides are lines too (when they stand one above the other, read left and right as up and down). For example, if the left 3 did not use its left side, it would use its top and bottom sides. Both dots at the ends of the middle line would then be full, leaving the right 3 only 2 side it could use. The sides straight on from the middle line are crossed. With a line there, the 3s, 2 of them, would have to use all 2 sides at the far end, and 3 lines would meet at that dot.
See the whole board
The 3s of Easy No.1 at row 2, column 1 and row 3, column 1. The top side of the upper 3, the side between them and the bottom side of the lower 3 are lines. Straight on to the right from the middle line (the top side of row 3, column 2) is crossed.
53 and 3 corner to corner
With 3 and 3 corner to corner, the 2 sides of each at the corner away from the dot where they touch, 4 sides in all, are lines. A 3 can leave only 1 side empty, so each 3 uses at least 1 of its 2 sides at the touching dot. That dot takes at most 2 lines, so each can use only 1 side there. That leaves the 2 sides away from the touching dot as lines.
See the whole board
The 3s of Easy No.2 at row 4, column 3 and row 5, column 2. The upper 3 has lines on its top and right sides, and the lower 3 on its bottom and left sides.
6A 3 next to a 0
A 3 next to a 0 has the side it shares with the 0 crossed, so its 3 remaining sides are lines. The 2 sides that carry that side straight on are lines as well. A line along the 3's top (or bottom) side cannot go on to the 0's side at the corner dot, and the side between them is crossed, so it can only turn away from the 3.
See the whole board
The 3 at row 3, column 4 of Easy No.1 and the 0 to its right. The 3's top, bottom and left sides are lines, and so are the 2 sides that carry the side between them up and down.
7A 3's corner closed in by crosses
When the 2 sides leading out of a 3's corner dot are both crossed, the 3 has lines on the 2 sides at that corner. If the loop passes through the dot, it can only turn along the 3's 2 sides. If it does not, all 2 sides are empty, but a 3 can leave only 1 side empty. It is the same thinking as a 3 in a corner, using the crosses like the edge of the board. A 3 touching a 0 diagonally is a common case of this shape.
See the whole board
Normal No.1, part solved (step 5 of Solving one 8×8 puzzle). The 2 sides leading out of the top left corner dot of the 3 at row 4, column 5, the one going up and the one going left, are both crossed. So the 3's top and left sides are lines.
8A line into a 3's corner
A 3 can leave only 1 side empty, so at any corner it uses at least 1 of the 2 sides there. If 1 line comes from outside to a 3's corner dot, at least 1 of the 3's lines also comes to that dot. A dot takes at most 2 lines, so the 3 can use only 1 side at this corner. So the 2 sides far from the corner are lines. The other 1 way out of that dot is crossed, even if it was not decided yet.
See the whole board
Easy No.12, part solved. A line comes down to the top right corner dot of the 3 at row 3, column 2 (the right side of the 1 at row 2, column 2). The side going right from that dot (the top side of row 3, column 3) is not decided yet. Even so, the 3's bottom and left sides, far from the corner, are lines, and the side going right is crossed.
9A 1's corner closed in by crosses
When the 2 sides leading out of a 1's corner dot are both crossed, the 1 has the 2 sides at that corner crossed. If the loop passed through the dot, it would run along the 1's 2 sides, making 2 lines, more than 1. If it does not, then of course all 2 sides are crossed. The edge of the board counts the same as a cross.
See the whole board
Normal No.3, part solved. At the top left corner dot of the 1 at row 1, column 4, above is beyond the board and the side going left (the top side of row 1, column 3) is crossed. So the 1's top and left sides are crossed.
10A line into a 1's corner
When 1 line comes from outside to a 1's corner dot, and the other 1 way out of that dot is crossed or beyond the board, the line runs along one of the 1's 2 sides at that corner. That uses up the 1, so the 2 sides far from the corner are crossed.
See the whole board
The same moment in Normal No.1. A line comes down into the top left corner of the 1 at row 7, column 5. The side going left is crossed. The line runs along the 1's top or left side, and that uses up the 1, so the right and bottom sides, far from the corner, are crossed.
113 and 3 on a diagonal with 2s between
On one diagonal, even with 2s between 3 and 3 (however many 2s in a row), each 3 at the ends has lines on the 2 sides at its far corner. A 3 uses at least 1 side at any corner, so the dot it shares with the next 2 can take at most 1 line from the 2's side. A 2 has at most 1 line at that corner, so at least 1 of its 2 lines is used at the opposite corner. This carries on to the next 2 and the one after, 3, until the 3 at the far end can use at most 1 line at its near corner. A 3 can leave only 1 side empty, so it uses exactly 1 side at the near corner, and the 2 far sides left are lines. The 3 at the other end is the same.
See the whole board
From the 3 at row 3, column 5 of Normal No.5, across the 2s at row 4, column 6 and row 5, column 7, to the 3 at row 6, column 8. Even on a board with nothing drawn yet, the top and left sides of the top left 3 and the bottom and right sides of the bottom right 3 are lines.
Questions
In what order should I look for patterns?
On a blank board, first look for a 3, 1 or 2 in a corner, 3 and 3 side by side, 3 and 3 corner to corner (even with 2s between them), and a 3 next to a 0. Once lines start to appear, look for corners closed in by crosses and corners a line comes into.
Do I have to memorise every pattern to solve them?
Easy puzzles can be solved just by counting each number's lines and extending them. Knowing the patterns helps you find the first lines quickly and get stuck less often.
Besides the patterns, are there any rules I can use right away?
Never closing a small loop early, and following the ends of lines (a dot has 0 or 2 lines). "Counting" in How to play explains them.
What if patterns alone won't solve it?
Hard also asks you to work out whether a square is inside or outside the loop, and Oni to try a line and see if it holds. Solving hard puzzles explains both on real boards.
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