How to Solve Slitherlink Puzzles
Slitherlink, sometimes called Fences or Number Line, originally appeared in the Japanese puzzle magazine Nikoli as Suriza Rinku. Your goal in this puzzle is to draw one and only one closed loop with horizontal and vertical lines between the grid dots.
- The loop cannot cross over itself.
- A number shows exactly how many lines must be adjacent to it. Note that the number itself may end up inside OR outside the loop.
- Spaces without a number may have any amount of adjacent lines, from zero to 3 (obviously not 4, because that would be a closed loop).
The best way to begin is to first look for any zeroes on the grid. Since there are definitely no lines around them, we can mark those connections out with an X, as shown here.
It is helpful to mark connections that can’t be used as you solve the puzzle, as it will make it easier to see what possible lines remain.
Since we have several 3 directly adjacent to those zeroes, we know that their remaining sides must have a line, since one of the four sides cannot have one.
After drawing those known lines, you can also mark out intersections that cannot contain lines, shown here with a red X. These must be marked out because our final loop cannot branch or cross itself, therefore there will never be three lines connecting at the same grid dot.
After drawing the boxes around the 3s that were adjacent to a 0, because we knew which way their open side faces, we also know that the loop will have to turn, because of that X around each side of the 0. This 3-0 pattern is one of many that you will learn as you solve more slitherlink puzzles.
Now, let’s draw the final line to complete the 3s in this puzzle, since we know the open side for all of them.
Another useful pattern to learn is when you have 3s that are horizontally or vertically adjacent. The open side cannot be between them, because you would form a closed loop. It can’t be at the far ends, because the “bottom” of the box for each 3 would share a side, and you would have branches, which aren’t allowed in our loop.
That means that you will always end up with a series of parallel lines between the 3s. You won’t know yet which side will have the open spaces, but it is helpful to know that when you see 3s next to each other, you can draw a few known lines.
Up at the top, we can draw this line to connect the two portions of the loop we have so far. I’m also placing a couple more Xs for places we can’t put a line because it would create a branch.
Next to the 2, our loop is going to simply follow the border down, because it can’t just dead-end where it is, and can’t turn the other way.
As for the other end of what we’ve drawn so far, over by the 3, we can see that it can’t turn left or right, so it must go straight ahead.
Note that in most puzzles, you will most likely be working on several different segments of your loop for a while, and won’t necessarily be able to connect them into a single line this quickly.
After extending that line, we’ll put an X below the 2, because it now has two sides, so there can’t be another one. This means the line on that side is going to go down and turn the corner at the bottom of the grid.
Now let’s take a look at the right side of the puzzle, by this 1. It has only two potential sides for a line, and here, I’ve marked the incorrect one. Notice that at one end of the segment, it would basically dead end, because the Xs above it prevent it from continuing or turning.
Try to look for patterns of Xs like this, as it will let you add an X between other dots to eliminate even more false line positions.
We’ve drawn in the lines discussed in the last step, as well as the X on the last side of the 2 in the bottom corner of the grid.
Looking at this final 1, it’s apparent that the side it needs is on the bottom, as it will simply extend the line under the 2 that cannot turn.
After that, we’ll be left with only a row of blank spaces, which can have any number of lines surrounding them.
Since we only need to connect the portions of the loop at this point, the final line segments are fairly obvious – simply draw a straight line along the bottom of the grid, turn up to connect to the green line under the 1 on the right, then left to completely close the loop.
After adding in those final line segments, we can now view the completed loop.
