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This is an example of a completed Slitherlink puzzle. A Slitherlink puzzle is a grid, and some
of the cells will contain number clues. The aim of the puzzle is draw a single loop around the grid
so that all the clues are satisfied. The clues tell you how many of its four sides are part of
the loop.

This is a Slitherlink starting grid. The most obvious place to start any Slitherlink puzzle is with
the '0' clues. You know that none of these sides form part of the loop, so you can put a 'x' on these
links.

This first initial step will give you other obvious clues. Take the highlighted '3' clue as an
example. One of the sides of this clue can't be part of the loop - the side with a 'x', so that must
mean that the other 3 sides are a wall. We can fill this in.

The next place to look is for a group of '3' clues. We have two adjacent '3' clues in the top
left corner of this puzzle. There are only two possible ways these two clues can be
satisfied. The loop can either go ABDEG, or it can go ACDFG, there are no other ways for both
clues to be satisfied. Both possibilities have A, D and G as walls, so we can
fill these lines in.

There is another block of '3' clues in the middle of this puzzle. There are a limited set of possibilities
for this type of diagonally connected '3' clues as well. The top-left cell has the possibility BAD or
ABC. If both C and D were walls, then it would mean that E and F couldn't be walls, which means that
there aren't enough surrounding sides to satisfy the '3' clue. Both of these combinations have A and B
as walls, which means we can fill those in.

We can apply the same rules to EFGH cell, and conclude that G and H must be lines. There are other
sets of diagonal '3' clues in this puzzle, and we can apply the same line of reasoning to all of them.

It can be equally useful to think about where we can't put walls. Look at 'A' and 'B' at this point.
Neither of these can be walls since the loop of walls around the puzzle can't intersect, or touch
at any point. This means we can insert a 'x' in these places across the whole puzzle.

Also, the highlighted '1' clues already have their one wall, so we can put a 'x' in for all the other
sides for these clues.

We have now arrived at this situation and can fill in more lines. 'A' and 'B must be walls to
satisfy the '2' clue. 'D' must be a wall to satisfy the '3' clue.

'C' is a little more subtle. If 'C' was a wall, then the only way the other '3' clues in this area
could be satisfied is to join this section in it's own small closed loop. This is against the rules
of the puzzle, so 'C' can't be a wall, and we should mark it with a 'x'. The '2' clue means that
the top and bottom sides must be walls.

We have now made more progress on this puzzle by continuing to apply the same logic of where walls
can go, and where they can't go. Now consider the area in the bottom-left of this puzzle. The wall
must exit this area in this way. There are two possibilities, it can either exit via ABCE, or go
directly with DE. If it follows DE, then the '2' clue will have three surrounding walls, so that
can't be possibility, so the wall must follow the ABCE path.

The '3' clue towards the bottom-right has the wall approaching from the right. There are only two
ways the wall can satisfy the '3' clue from here, either HKF, or GFK. Both of the possibilities have
F and K as walls, so we can fill these in.

We have now arrived at this position. There is only way for the pair of '2' clues to be satisfied
here, and that is if the wall loop follows the path ABC between them.

You now have all the techniques you need to solve Slitherlink puzzles!

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Odd Even Sudoku

SudokuXV

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