Links strategy: squeezed cells, narrow passages and the what-if

In Links, the lines you're sure of rarely start at the numbers. They start in the cells nobody seems to want: corners, edges and pockets that some line has to pass through, and can only reach one way.

How the difficulty works

Each tier is set by the hardest step you'll need:

• Easy (6×6) needs only the basics: squeezed cells, finished cells, and links that would join two different numbers or close a loop.
• Medium (8×8) needs at least one narrow passage: a cell that every way between a pair has to go through.
• Hard (10×10) needs a short what-if.

The basics

Every cell without a number has a line passing through it: one way in, one way out. A number is the end of its line, so it has one way out. Four moves follow from that, and soon become automatic:

• Squeezed: a cell with only as many ways out as it needs — two for an empty cell, one for a number — uses them all.
• Finished: a cell that already has its line, in and out, is closed to every other line.
• Different numbers: a link that would join the line from one number to the line from another is impossible.
• No loops: a link that would close a line on itself is impossible too, because every line must end at its two numbers.

Squeezed cells

Corners are the classic case, with only two neighbours to begin with. Edges come next. As lines fill in, cells in the middle get squeezed too, so after every few links, look around them again.

Lines that mustn't meet

Every time you draw a piece of line from a number, it carries that number with it, and its free end can only ever meet its own partner. A cross like this one often squeezes the cells beside it.

No loops

Pieces of line you draw in the open will meet up as the puzzle goes on. Never join the two ends of the same piece: it would close into a loop that can't reach a number.

Medium: narrow passages

Pick a pair and look at the ways its line could still go, from one number to the other without crossing anything. If every one of them passes through the same cell, that cell is on its line — even if you can't yet say how the line gets there.

The same question works the other way round. Every cell has to be filled by some line, so look at a pocket of empty cells and ask which numbers could get a line in and out again. When only one can, the pocket is part of its line. Small numbers in the corner of a cell are a good way to keep track.

Hard: a short what-if

On Hard puzzles you'll sometimes find nothing squeezed and every cell reachable by more than one number. Then pick a spot with two choices — a link there or not — and ask what happens with one of them. Follow it only a few steps: a cell with no way out, a pocket no line can reach, two numbers forced together. If it breaks, the other choice is right.

Try the choice that looks like it will fail fast. A what-if that doesn't break within a few moves isn't proving anything; take it back and look elsewhere.

Good habits

• Corners and edges first. Fewer neighbours means fewer choices.
• Watch the pockets. A group of empty cells walled in by lines must still be filled — by a line that can get in and out again.
• After each link, look at both ends. The cells beside it have just lost a way out.
• Don't race to the partner. The shortest route between two numbers is rarely the answer, because every cell on the way has to be used by someone.