Draw lines through the middles of the squares, never diagonally, using every square. Lines may not cross or branch, so a square without a number takes one line in and one out. No line crosses a wall, a thick bar between squares. What the numbers ask depends on the game mode:
On a touch screen, a tap does what a click does, and a long press what a right-click does (more ways to right-click).
Drag from square to square to draw a line along the edges you pass. A drag only adds: passing back over a square it has already drawn through does nothing, and it carries on once you return to where it reached, so a long line can be drawn in one stroke. Undo takes a stroke back. A drag along a line you have drawn and on past its end carries that line on, and a drag that runs only along lines you have drawn takes them up. A line stops where it would give a square more lines than it takes, where you have crossed the edge out, or at a wall. You can also click near the edge between two squares to draw or remove a line there.
A stroke that starts on a number draws that number’s line again: when you let go, the line that ran on from the number before is taken up, as far as it went, and your stroke is drawn in its place. In Path the line that leads into the number from a lower one stays, so a stroke from the 2 keeps the line from the 1 and replaces everything on from the 2. In Pairs the number’s whole line is replaced.
Right-click an edge to cross it out, to mark that you are sure no line goes there, and keep the button down and drag to cross out every edge you pass. Right-click it again to clear the cross. A wall cannot be crossed out or cleared. You never need to cross anything out to finish.
The keyboard can also be used. The arrow keys move a cursor. Press Enter to start a line, move the cursor along the way you want it (moving back along it takes a step back), and press Enter again to draw it; Space, Escape, Backspace or Delete abandons it instead. Holding Ctrl while pressing an arrow key draws or removes the line in that direction and moves along it, holding Ctrl and Shift together does the same without moving, and holding Shift alone crosses out or clears the edge in that direction.
In Path, the color runs along the line from the 1 to the highest number: each stretch of line between two numbers takes a color of its own, in order round the color wheel, and each number is ringed in the color of the stretch that leaves it, the highest in that of the stretch that reaches it. A number’s disc fills once the line reaches the numbers either side of it.
In Pairs, each pair of numbers has a color, ringing both its numbers, and a line takes that color once it reaches one of them. Colors repeat on a board with more pairs than colors, and the numbers tell those pairs apart. A pair’s two discs fill with its color once a line joins them.
In both, a line that reaches no number yet has no color. A line turns red when it breaks the rules already: when it closes into a loop, or joins two numbers that may not meet. In Path that is two that are not one apart, such as a line from the 3 that reaches the 5 before the 4, and in Pairs two different numbers.
The puzzle is solved when every square has its lines and they join the numbers as the mode asks. Every puzzle has exactly one solution, and none needs a guess.
Path is the puzzle LinkedIn publishes daily as Zip. Pairs is Nikoli’s Numberlink, also published as Arukone, and played by many as Flow Free. Simon Tatham wrote a generator for it but never a game; this one fills every square, as Flow Free does.
Hint explains the next step rather than simply making it. It reasons only from the numbers, the walls and the lines and crosses you have drawn, so it carries on from wherever you are, as long as none of those is wrong; if one is, it asks you to fix the highlighted mistakes first.
An edge beside a square that already has all its lines can never take another, and neither can an edge whose line would join two numbers that may not meet, whether the numbers sit beside it or lines lead to them from it. In Path, neither can an edge whose line would close a loop. The hint counts all of these as closed without asking you to cross them out, and most steps are then one rule at work: a square with only as many open edges left as it still needs lines takes a line on each of them.
On Normal boards a step sometimes looks at what a line would do, drawing it thin. A line breaks the board if it leaves a square a dead end or cut off, closes a loop, or joins two numbers that may not meet. An edge whose line would break the board is crossed out. A square that needs two more lines and has three open edges left takes the third if lines on the other two would break the board.
On Tricky boards a square that needs two more lines and has all four edges open has to be weighed whole. If lines on any two of three of its edges would break the board, the fourth takes a line; and an edge whose line would break the board beside any of the square’s other edges is crossed out. Each way is looked at on the board as it stands, so nothing needs following further.
These parameters are available from the ‘Custom type…’ option on the ‘Type’ menu.
Easy puzzles can be finished one square at a time: a square with only as many open edges as the lines it still needs takes a line on each.
Normal puzzles also need you to see that a line, or a square's two lines, would break the board at once.
Tricky puzzles need you to weigh every way a square with four open edges could take its two lines.
Unreasonable puzzles have one answer, but may need you to try a line and follow it to see where it leads.