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Puzzle Quarry

Slitherlink

Choose a size and a level and a fresh board of dots and numbers is built in your browser, checked, and put on screen. No limit, no account, nothing uploaded.

Medium Time 0:00 Segments 0/52

211222211313113211200131300230

A medium 8×8 board with 30 numbers. Click a segment once to draw it, again to cross it out.

Check this before you rely on it. This slitherlink generator is provided free and without warranty, and its results are not professional advice.

One loop, and the numbers that describe it

The board is a lattice of dots with numbers scattered in the squares between them. Your job is to draw a single closed loop along the segments joining neighbouring dots, so that every number ends up with exactly that many of its four sides used by the loop. A 3 has three of its sides on the loop and one off; a 0 has none at all; a square with no number in it is unconstrained and might have any amount of loop around it.

What makes it a puzzle rather than an arithmetic exercise is that the loop has to be one loop. It may wander anywhere, it may be as long and as convoluted as it likes, but it has to come back to where it started without ever branching and without ever crossing itself. Stated at the dots that is a startlingly simple condition: each dot has either nothing touching it or exactly two segments.

Those three sentences are the whole game. Nothing is hidden behind them, there are no regions or blocks or colours, and every board on this site is decided by the interaction of the numbers with the shape of a curve.

Why the empty squares matter as much as the numbers

Beginners read a slitherlink as a set of numbers with gaps between them. Experienced solvers read it as a curve with numbers annotating it, and the difference in speed is enormous. A number tells you about four segments; the curve tells you about the whole board, because wherever it goes it has to come back, and every dot it touches sends it onwards.

That is why a board with very few numbers is not necessarily harder than one covered in them. Numbers constrain the curve locally, but the requirement to close constrains it globally, and a sparse board often has a very tightly determined shape. Some of the most pleasant boards here carry a number on barely a third of their squares.

It is also why crossing segments out is not optional bookkeeping. Knowing that the loop does not use a particular segment is exactly as informative as knowing that it does — it takes a way out away from two dots and takes a side away from two numbers — and a board where eliminations are only held in the head is a board you will solve three times over.

What actually makes one board harder than another

Not from the size and not from how many numbers are missing. A 12×12 with an obvious opening is a long sit rather than a hard one, and a 5×5 with one genuine bottleneck can take longer. The four levels here name the reasoning a board forces on you instead.

Easy is finished with the two rules you would work out for yourself in the first minute: what a number says about its own square, and what a dot says about the line passing through it. Medium adds the corners, where a dot has only two segments to offer and that alone settles the number sitting in it. Hard makes you read two threes against each other. Expert is where the closing rule decides it — where a segment is impossible only because drawing it would seal a short ring while numbers elsewhere are still unsatisfied.

The grade is measured rather than estimated. Every published board is solved by a program that applies the cheapest argument that fits, over and over, and the hardest one it was ever cornered into is the level printed on the board. A board built for one level that turns out to need another ships under the level it measured — an honest label beats a flattering one.

Common questions

What is a slitherlink puzzle?

A grid of dots with numbers between them. You join dots with straight segments to form one closed loop, and every number must have exactly that many of its four surrounding segments on the loop.

Can the loop cross itself or branch?

Never. Each dot carries either nothing or exactly two segments, which rules out both at once — three segments at a dot is a branch and four is a crossing.

Does every square need a number?

No, and most boards number well under half of them. A square with no number simply places no constraint on its own four sides; the loop is pinned down by everything around it.

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