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How to play Slitherlink

Slitherlink is a wonderfully pure logic puzzle which doesn't require you to learn any complex rules. To solve a puzzle:

  • Draw a single loop on the puzzle grid, such that the loop doesn't touch or cross itself at any point.
  • Wherever a number appears in the grid, the loop must pass by that many sides of the square with the number in.

If, for example, a square in the grid has a '3' in it then that square must have 3 shaded sides, and all those shaded sides must form part of the single loop. If a square has a '0' in it then there must be no parts of the loop neighbouring the square. Not all squares have numbers in - how many times the loop neighbours these squares is left for you to deduce as you solve the puzzle.

Here's an example puzzle:

There are various places you can start solving this puzzle. Although the ultimate aim is to mark in the shaded segments that make up the loop, it's very useful to make a note of which segments can't contain any part of the loop. The '0' squares indicate some of these clear segments straight away, so we can begin by marking these in.

On puzzlemix you simply right-click or ALT-click to mark segments as clear, remembering that you can also drag the mouse if you want to select multiple segments or are having problems clicking accurately enough. I have marked them pink here so that they show up clearly in these pictures:

If you look at the '3' nearest to the top-left, you can see that there are only 3 remaining sides that can be shaded, since the neighbouring '0' precludes the bottom side from being shaded. So we can shade these 3 sides in right away, since we are certain they must form part of the loop we are searching for.

Because we know there is only one loop, we know that the two ends of the three-segment path we have drawn must be connected to something else, so we can extend the loop either side of the '3'. We also know the loop can't cross or overlap itself, so the top side of the second '3' must be empty. We can then extend the loop further still using this and similar logic:

At the top-left the loop cannot go left or up from here. The up option is eliminated because we already have '2' sides shaded, but the option to the left can be excluded because the loop would have nowhere to go if it went left here. So it must go down.

Looking also at the '0' in the left-most column, we can see that there is only one possible solution to the '2' directly below it. If we shade that only solution in and extend it in the only way it can be extended, we end up with this result:

At this point there are then a series of further extensions of the loop that can be made by going back and forth between the two loop segments we are building. You can start by observing that the '2' in the third row of the second column can only be solved using its top and right-hand sides, and then continuing from there. The result of stepping further using relatively simple logic is as follows:

At this point although it is possible to progress these line segments using more complex reasoning, by far the easiest way to continue the puzzle is to look at another area. Let's consider the two '3's at the top-right.

A '3' in the corner of a puzzle must have its two corner-most segments shaded, otherwise the loop would not be able to extend through it. If we mark these in at the top-right and then consider how it must interact with the '3' immediately below it, we can shade in segments as shown here in dark purple:

Corners and other restricted areas of the puzzle are often useful places to look when you're stuck. A '3' with two neighbouring 'exits' blocked can always have those two sides shaded in the same way as applies when it is in the corner of the grid.

The two '3's diagonally next to one another in the penultimate and last columns are also interesting. Experimentation on a piece of paper will show that all solutions to '3's arranged like this involve shading in the two outer-most line segments on both squares, rather like shading the top and bottom of a figure '8' if you were to look at the puzzle from a diagonal angle. By shading these in and extending both these segments and those on the '3's at the top-right, we end up with this result:

At this point there are various places you can progress, using slightly more complex logic. The '2' square at the bottom-right cannot be shaded to the top and left because the '1' square next to it would then have no remaining sides to be shaded, and the loop would not be able to 'escape' from the bottom-right corner. So the solution must go via the right and bottom-hand sides.

At the bottom-left, experimentation with the '2' and '3' will reveal there is only one possible solution. Continuing in a similar vein will soon result in the final solution:

The final solved puzzle, redrawn without the colours, looks like this:

Good luck! Slitherlink can sometimes be a very challenging puzzle, but it can also be a wonderfully rewarding puzzle. As you play it more and more you will begin to spot more and more patterns - but you'll probably never find it universally 'easy'!

On the right of the puzzlemix player you might notice the ability to change colours.. Although this is purely decorative and so you are welcome to ignore it, it can be very useful when solving the puzzle in order to make notes or try out test solutions. There is no difference between the colours so far as the correct/incorrect status of the puzzle is concerned, but using different colours has the additional advantage that if you decide against a test solution you can simply 'del'ete all segments of a colour in a single click. You can also 'fix' a colour to convert it into black and white if you decide it is correct (although you don't need to do this to be judged to have solved the puzzle correctly). You can of course also always use the 'undo' button or press 'Z' to undo moves at any point - this will even undo deleting and fixing colours. You can also 'redo' any or all changes you decide against 'undo'ing!

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