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Puzzle Quarry

Slitherlink Solving Techniques

Five arguments, and the order matters more than the list. Whichever is the hardest one a board corners you into is the difficulty printed on it — here, and in the code.

Ordered by what it costs a person

The ladder is an order to try things in rather than a list of tricks to memorise, and its order is not the order a machine would pick. The two rungs at the bottom are the ones nobody has to be taught: read a square against its number, and follow a line through a dot. They come first because they are what your eye is already doing, and because every deduction above them gets cheaper once they have been exhausted.

That last point is the practical one. Reading two threes against each other on a board where nothing else has been done means holding eight segments in your head; the same pair after one more sweep of the dots may have half of them settled already and answer itself. Players who describe this puzzle as fiddly are almost always doing the expensive move while a free one is still on the table.

One placement in this ladder is worth defending, because it is the one anybody who knows the puzzle will query. The dot rule sits second, right beside the arithmetic, rather than up among the named patterns. As a piece of theory it is the rule the entire puzzle rests on and it looks like it belongs at the top. As a move it is the cheapest thing on the board, and grading it as difficult would have made every board on this site expert — a scale on which everything scores the same is not measuring anything.

Where the label on a board comes from

Every published board is run through the same solver the hint button uses. It applies the cheapest argument that fits, over and over, until every segment is decided, and it records the highest rung it ever stood on. Easy stops at the two local rules. Medium reaches a corner. Hard reaches a pair of threes. Expert reaches the closing argument.

Nothing is graded by how many numbers were left off and nothing is relabelled afterwards. The check runs at both ends of the band, too: a board can come out easier than the level asked for, and — less obviously — a board with a number on every single square can already need more than the level allows, in which case the carve has nothing it may remove and the result is thrown back. Ask for medium on a 5×5 and you will occasionally be handed an easy board, because five columns do not always leave room for a corner to be the deciding factor.

There is a sixth rung and nothing here is allowed to stand on it. Drawing a segment, following it until something breaks and rubbing it out will finish any board whatsoever, which is exactly why it cannot be part of a difficulty scale. Its page explains what it is and why every board needing it is discarded.

Common questions

How many techniques does a slitherlink need?

Five, and most boards need three of them. The two local rules finish an easy board on their own; the corner cases, the pair of threes and the closing argument are each what one further level of difficulty means here.

Which slitherlink technique should I learn next?

Whichever one your current level stops at. Stalling on medium means the corners are not yet a tool you reach for; stalling on expert means the closing argument is not. The hint names the argument it used, which is the quickest way to find your own gap.

More Slitherlink pages