How to play

Every number appears twice on the grid. Draw a line from each number to its twin, moving from square to neighbouring square — never diagonally — so that no two lines cross or touch, and when you are done, no square is left empty. That last rule is the whole puzzle: with every square spoken for, there is exactly one way to lay the lines, and every deduction you make comes from working out which line must be the one to pass through a particular square.

Press on a number and drag to draw its line. Drawing over another line cuts it off from that square on; dragging back along your own line rewinds it. Tap anywhere on a line to cut it back to that point.

Controls

• Click / drag — draw a line from a number, or pick a line up where you left it
• ↑ ↓ ← → — move the cursor
• Space or Enter — start drawing from the square under the cursor; the arrows then extend the line
• Backspace — while drawing, take the last square back
• Esc — stop drawing
• Z or U — undo
• H — use a hint (3 per puzzle; lays down one whole pair)
• R — restart the puzzle

Strategy tips

• Start at the edges. A square on the border has only three neighbours, and one in a corner just two — a corner square that is not itself a number must be a bend, and the line through it can only come from its two neighbours.
• Watch the pockets. Any square with only one free neighbour is a dead end nothing can pass through, so a line must end there — and since lines end only on numbers, that square's neighbour has to be routed so the pocket disappears.
• Twins next to each other are a trap. Two matching numbers side by side could be joined directly, but that would strand the squares around them. The line has to take the long way round and sweep those squares up.
• Long lines hug the walls. The pairs that sit far apart usually run along the outside; get those in first and the middle of the grid falls into short, obvious connections.
• Never guess. Every puzzle here has exactly one solution, so if two routes both look possible, one of them leaves a square empty somewhere else. Find that square.

About Numberlink

Numberlink is one of the oldest paper puzzles still in print — a version by the American puzzle-maker Sam Loyd appeared in 1897 — and it has run in the Japanese magazine Nikoli since the early 1990s. The same rules reached hundreds of millions of phones in 2012 as the colour-dot game Flow Free, which is where most people meet it today.

This edition ships 750 puzzles: 300 at 5×5, 250 at 7×7, and 200 at 9×9. Each grid is built by laying its solution first and then handing the numbered endpoints to a solver that counts every way to fill the grid. Only grids with exactly one filling are kept, so nothing you play here ever needs a guess. Within each size the puzzles are ordered by how many choices the solver had to weigh, so #1 is the gentlest.