How to solve Numberlink: connecting every pair, filling every cell

The rules

• Connect each pair of equal numbers with a single path.
• Paths move between cells through their sides, never diagonally.
• Paths never cross or branch.
• Together, the paths fill every cell of the grid.

Start with short pairs and edges

• A pair whose numbers sit next to each other or very close usually connects directly; anything longer would waste space other paths need.
• Pairs on the border have fewer directions to go. A path that hugs the edge or a corner rarely blocks anyone else.
• A number in a corner has only two ways out; if one is blocked, its path must take the other.

Forced cells

Look for cells that only one path can reach. A cell boxed in on three sides by finished paths or walls must be part of the path that passes its open side; otherwise it would stay empty. The same goes for a narrow corridor one cell wide: whichever path enters it must run all the way through.

Don't leave pockets

The commonest mistake is a path that cuts off a small area which no other path can reach. Before you commit to a long path, check that every region it separates still contains both numbers of some pair, or can be filled by a path that passes through it.

A solving routine

1. Join adjacent and nearby pairs.
2. Run paths along the border and into corners.
3. Fill corridors and boxed-in cells with the only path that can reach them.
4. Check that no region is left without a path to fill it.
5. Stretch the remaining paths to cover every empty cell.

Practise

On Puzzimo, drag from a number to its partner to draw a path; drawing over another path cuts it, and undo is free. Any set of paths that connects every pair and fills the grid wins, even if it differs from the one the generator had in mind. Grids come in 5×5, 7×7 and 9×9, with a 7×7 daily challenge.

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