Loop Puzzle (Slitherlink): 8×8, 1 Puzzle Solved from Start to Finish
Here the free puzzle Normal No.1 of the Loop Puzzle (same rules as Slitherlink) is solved in 9 steps, from a blank board to one closed loop. Every step shows the board as it stood when solved in that order. The rules and the names of the ways to solve are in How to play.
This article's puzzle
Rows count from the top and columns from the left. "The 3 at row 2, column 1" means the 3 in row 2 from the top, square 1 from the left. In the pictures, violet lines are drawn lines, and a grey × marks a side with no line.
1Start with the 0 and the 3 and 3 at top left
Start with what catches the eye. The 0 in the top right corner has no line on any of its 4 sides, so they are all crossed. Where a dot beside the 0 has only 1 way left, that side is crossed too. A dot has 0 or 2 lines, so there can be no dead ends.
At top left there are 3s stacked one above the other, 2 of them. With 3 and 3 side by side, the side between them and the outer sides above and below are always lines. The side straight on from the middle line (the bottom side of row 1, column 2) is crossed.
The line along the top side has come into the dot at the top left corner. It is a corner of the board, so the only other way is the left side. That is a line too.
Used here: Cross every side of a 0 3 and 3 side by side A dot has 0 or 2 lines
2Count along the top
From here, count each number's lines. The 3 at row 1, column 1 has its 3 lines on the top, left and bottom, so its right side is crossed. Where the end of a line has only 1 way to go, it goes that way. The 1 at row 1, column 2 has a line along its top. That uses it up, so its other sides are crossed.
To its right, the 3 at row 1, column 3 has its left side crossed, so the 3 sides left are all lines. As crosses build up, the 2 at row 1, column 4, the 2 at row 2, column 4 and the 2 at row 3, column 2 also have just as many free sides as lines they still need. In each case the remaining sides are all lines.
Used here: Counting a number's lines A dot has 0 or 2 lines
3On to the top middle
The 2 at row 2, column 5 is crossed above and below and has a line on its left. The only place for line 2 is the right side. To its right, the 1 at row 2, column 6 is used up by its left side, so its other sides are crossed.
The 2 at row 3, column 4 reaches 2 lines with its top side and the left side that grew there by the dot rule. Its bottom side is crossed. This cross comes into use in step 5. At the dots at top right, more crosses follow so that no dead end forms.
Used here: Counting a number's lines A dot has 0 or 2 lines
4No small loop in the left column
Look at the left column. The two ends of the one line that came round the top left now face each other across the top side of row 4, column 1. Drawing it would close a small loop. There is only one loop, so that side is crossed (never close a small loop).
Both ends can only go down, so the left and right sides of row 4, column 1 are lines. They then face each other again across the top side of row 5, column 1, so that side is crossed too.
Used here: Never close a small loop A dot has 0 or 2 lines
5A 3's corner closed in by crosses
Look at the 3 at row 4, column 5. The 2 sides leading out of the dot at its top left corner (the one going up, and the one going left that was crossed in step 3) are both crossed. If the loop passes through this dot, it can only turn along the 3's top and left sides. If it does not, the top and left sides are both empty, but a 3 can leave only 1 side empty. So the top and left sides are lines. It is the same thinking as a 3 in a corner, using the crosses like the edge of the board.
The dot rule crosses the 3's right side, and the bottom side left is line 3. Directly below, the 1 at row 5, column 5 is used up by its top side, so its other sides are crossed.
The 2 at row 4, column 6 is crossed on top and left, so its bottom and right sides are lines. The 2 at row 5, column 4 and the 2 at row 5, column 7 also have 2 sides blocked by crosses, so the 2 sides left are lines.
Used here: A 3's corner closed in by crosses Counting a number's lines A dot has 0 or 2 lines
6Count the 2s on the left
The 2 at row 6, column 4 reaches 2 lines with its top side and the right side that grew there by the dot rule, so its bottom side is crossed. The 2 at row 5, column 3 is crossed above and below, and the only side it can use besides the line on its right is the left. The 2 at row 6, column 3 is crossed on top and right, so its left and bottom sides are lines.
Next, the 2 at row 6, column 2 is also crossed above and below, and the left side, the only one left besides the line on its right, is line 2.
Used here: Counting a number's lines A dot has 0 or 2 lines
7A line into the corners of 3 and 1
Here the shapes at 3 corners can all be used at once. The 3 at row 4, column 8 has a line coming up into its bottom left corner, and the side going left is crossed. The line turns onto the 3's left or bottom side, so the top and right sides, far from the corner, are lines (a line into a 3's corner).
The 3 at row 6, column 6 has both 2 sides outside its top left corner crossed, so its top and left sides are lines (the same shape as step 5). A line also comes into its top right corner from the right, and the side going up is crossed, so the far bottom side is a line too. That makes 3 lines, so its right side is crossed.
The 1 at row 7, column 5 has a line coming down into its top left corner, and 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 far right and bottom sides are crossed.
To its right, the 2 at row 6, column 7 has its bottom side left as line 2. The 1 at row 7, column 5 also has its top crossed by the dot rule, and its left side is settled as a line.
Used here: A line into a corner A 3's corner closed in by crosses Counting a number's lines
8Finish the bottom right corner
The 3 at row 7, column 8 also has a line coming into its top left corner from the left, and the side going up is crossed. The far bottom and right sides are lines. These 2 lines join at the top right dot of row 8, column 8, so the right side of row 8, column 8 is crossed. The dot at the bottom right corner would be a dead end, so the bottom side is crossed too. The 2 at row 8, column 8 can use only the left side besides the line on top, so that is a line.
The 2 at row 8, column 7 has its 2 lines, so its left side is crossed. The 3 at row 7, column 8 has its left crossed, and the top side left is line 3. The 3 at row 4, column 8 also has a line reaching its bottom side, which makes 3 lines, so its left side is crossed. To its left, the 2 at row 4, column 7 has a line on its top side.
Used here: A line into a corner A dot has 0 or 2 lines Counting a number's lines
9Close the loop at bottom left
What is left is the bottom left. On the bottom row, the two ends of the line face each other across the left side of row 8, column 5. Drawing it would close a small loop, so it is crossed.
The 2 at row 8, column 3 is crossed on top and right, so its left and bottom sides are lines. Once more, cross the left side of row 7, column 2 so that no small loop closes. The 2 at row 7, column 1 reaches 2 lines and its bottom side is crossed. Join the remaining lines by the dot rule and the one loop is complete.
Used here: Never close a small loop Counting a number's lines A dot has 0 or 2 lines
One loop, complete
When every side is decided, one loop meets every number. All this puzzle used was 0s, 3 and 3 side by side, a 3's corner closed in by crosses, a line into the corners of 3 and 1, counting each number's lines, the dot rule, and never closing a small loop.
At every step, the trick is this: once you add a cross, look again at the numbers and dots beside it. With each cross, more sides get decided.
Questions
Where do I start on a loop puzzle?
Start where a line or a cross is decided at once, such as a 0 or 3 and 3 side by side. After that, extend the lines by counting each number's lines and using the dot rule. In this article's puzzle, steps 1 and 2 alone decide 38 of the 144 sides.
What if I can't find anywhere to draw a line?
Add crosses as you go. More crosses leave fewer sides around a number that can take a line, and you reach places where all that remain must be lines. Also look for a 3 with a corner closed in by crosses on the outside.
What do puzzles harder than 8×8 need?
Hard (10×10) also asks you to work out whether a square is inside or outside the loop. Oni (12×12) also asks you to try a line and see if it holds. Solving hard puzzles explains both.
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