Numberlink: rules and how to play

Goal of the game

Join each pair of matching numbers with a continuous path and cover all 36 cells of the planned 6×6 board. Numbers identify pairs; they do not specify path lengths.

Rules

• Paths move between side-neighbouring cells, horizontally or vertically, never diagonally. A path joins exactly its two matching endpoints.
• Paths cannot cross, share a cell, branch or pass through a different pair’s endpoint. Every cell must belong to one path.
• This variant also forbids a path from touching itself along a side except between consecutive cells. Folding back beside an earlier part would create an extra connection.
• Each endpoint has exactly one same-path side-neighbour. Every other path cell has exactly two. Separate loops and detached fragments are not valid paths.

A small example, step by step

1. Take an endpoint in the top-left corner. Its only board neighbours are the cell to the right and the cell below.
2. Suppose the right-hand cell is already occupied by another confirmed path.
3. The endpoint has only one exit: its path must extend down.
4. Continue checking the new path end and the remaining empty area. Reaching the matching number is not enough if it leaves cells that no path can cover.

Beginner deductions

• Start with endpoints having only one available side-neighbour.
• A non-endpoint corner cell must connect through both of its two board neighbours, so a path must turn there.
• Look for narrow passages needed to connect separated areas. Avoid closing a route that strands another pair or leaves an empty pocket. Only commit a route when the constraints force it; a short route is not necessarily correct.

Common mistakes

• Do not stop when all pairs are connected if any cell remains empty.
• Do not cross diagonally or join two different labels.
• Do not fold a path back alongside itself: an extra side-contact changes its connections, even if the drawn line looks separate.