Number Loop, also called Slitherlink, is a logic puzzle played on a grid of dots. You draw one single closed loop along the edges between the dots so that each numbered cell is bordered by exactly that many loop edges. The loop never crosses or branches, and when finished it forms one continuous unbroken ring.

How do you start a Number Loop puzzle?

Begin with the zeros, since a 0 means none of its four sides are used, so you can cross all four off at once. Then work the forced pairs: a 3 next to a 0, two 3s side by side, and clues in the corners all lock edges immediately. From there each edge you place or rule out cascades into the neighbouring cells.

What does each number mean in Number Loop?

Each number tells you exactly how many of that cell's four sides are part of the loop. A 0 uses none of its sides, a 3 uses three of its four, and a 1 uses just one. Cells with no number can be bordered by any number of loop edges, so they carry no count constraint of their own.

What is the two-ends rule in Number Loop?

Every dot on the grid must have either no line ends meeting it or exactly two, because the loop either passes straight through a dot or misses it entirely. A dot can never have one, three or four line ends, since that would dead-end, branch or cross the loop. Checking this after every move keeps your lines connected into a single path.

Does solving Number Loop ever require guessing?

No. A well-made Number Loop has exactly one solution reachable by pure logic. Every Puzzle Lair Number Loop is generated and verified to be solvable without guessing, so being stuck means there is a deduction you have not spotted yet, often a two-ends check at a dot or a stray circuit the single-loop rule would forbid.

Solving guides

From the rulebook

How to Solve Number Loop

Number Loop, better known to many solvers as Slitherlink, asks you to draw a single closed loop along the edges of a grid. Each numbered cell tells you exactly how many of its four sides the loop uses, and the loop never crosses or branches. Those clues feel sparse at first, but each edge you rule in or out cascades through its neighbours. This guide takes you from the rules to the techniques that crack hard grids without guessing.

Play Number Loop

The rules of Number Loop

A Number Loop grid is a lattice of dots joined by short dotted edges. Your job is to draw one single closed loop that runs along those edges, never crossing itself and never branching. When you finish, the loop is one continuous unbroken ring, with no loose ends and no separate smaller loops anywhere on the board.

Scattered through the grid are numbered cells. Each number tells you exactly how many of that cell's four sides are part of the loop, so a 0 has no loop edges around it, a 3 has three of its four sides used, and a 1 has just one. Cells with no number can be bordered by any count. Every move comes from turning these counts into edges you can rule in or rule out.

Start with the zeros

Zeros are the strongest clues on the board, so start there. A 0 means the loop touches none of its four sides, so mark all four with an X straight away. That single act often forces edges in the neighbouring cells, because an edge ruled out on one side of a clue is also ruled out for the cell sharing it.

After the zeros, look for clue pairs that force edges. A 3 sitting next to a 0 must use the three sides away from the 0, since the side they share is already crossed off. Two 3s side by side force the edge between them plus the outer edges, and a 3 in a corner of the grid fills both of its outer corner sides. These opening patterns give you the first confident lines to build from.

Keep every dot to zero or two ends

The loop rule has a quiet partner that does as much work as the clues: every dot is a junction where the loop must pass straight through or not at all. That means each dot has either no line ends meeting it or exactly two. A dot can never have just one line end, because the loop would dead-end there, and it can never have three or four, because the loop would branch or cross.

Use this in both directions. If a dot already has two line edges, cross off its remaining edges, since no third line may meet it. If a dot has three of its four edges crossed off and one line already entering it, the last edge must be a line so the dot reaches two ends. Running this two-ends check after every placement is what keeps lines connected and turns scattered clues into a single growing path.

Propagate edges through the grid

Number Loop is a puzzle of cascades. Once a clue is satisfied, every other side of that cell must be crossed off, which feeds the two-ends check at its corners, which forces edges in the next cell along. Whenever you place or cross off an edge, immediately ask what it forces in the cells and dots that share it, then follow that chain as far as it runs before looking for a fresh start.

A 1 next to an edge you have already ruled in must use that edge as its single side, so cross off its other three. A 2 with two sides crossed off must use its remaining two, and a 2 with one side ruled in and one ruled out splits into two cases you can often test against a neighbour. The grid unravels edge by edge, each deduction opening the next.

Use the single-loop rule to finish

The strongest endgame tool is the single-loop rule itself. Because the answer is one closed loop, you can rule out any edge that would seal off a small separate circuit before the rest of the grid is joined. If drawing a particular edge would close a little ring on its own, that edge must be crossed off, since the finished loop has to be one connected piece.

Apply the techniques in order: cross off the zeros first, lock the forced corner and adjacent-clue edges, run the two-ends check at every dot, propagate each edge through its neighbours, then use the single-loop rule to kill stray circuits as the loop nears completion. On Puzzle Lair every Number Loop is guaranteed solvable by logic alone, so if you are stuck there is always a deduction waiting, never a guess. The big 10 by 10 boards are what make the hard set a genuine workout.

Frequently asked questions

What is Number Loop?: Number Loop, also called Slitherlink, is a logic puzzle played on a grid of dots. You draw one single closed loop along the edges between the dots so that each numbered cell is bordered by exactly that many loop edges. The loop never crosses or branches, and when finished it forms one continuous unbroken ring.
How do you start a Number Loop puzzle?: Begin with the zeros, since a 0 means none of its four sides are used, so you can cross all four off at once. Then work the forced pairs: a 3 next to a 0, two 3s side by side, and clues in the corners all lock edges immediately. From there each edge you place or rule out cascades into the neighbouring cells.
What does each number mean in Number Loop?: Each number tells you exactly how many of that cell's four sides are part of the loop. A 0 uses none of its sides, a 3 uses three of its four, and a 1 uses just one. Cells with no number can be bordered by any number of loop edges, so they carry no count constraint of their own.
What is the two-ends rule in Number Loop?: Every dot on the grid must have either no line ends meeting it or exactly two, because the loop either passes straight through a dot or misses it entirely. A dot can never have one, three or four line ends, since that would dead-end, branch or cross the loop. Checking this after every move keeps your lines connected into a single path.
Does solving Number Loop ever require guessing?: No. A well-made Number Loop has exactly one solution reachable by pure logic. Every Puzzle Lair Number Loop is generated and verified to be solvable without guessing, so being stuck means there is a deduction you have not spotted yet, often a two-ends check at a dot or a stray circuit the single-loop rule would forbid.

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