Solving techniques

The beginner's guide teaches the habits; this page names the deductions. Roughly in the order you'll need them as boards get harder.

1. The forced corner

A corner square has two neighbours, so any pipe passing through it must use both. If a corner holds a dot, its pipe leaves by one of the two — and if one neighbour is already claimed, the exit is decided. If a corner is empty, the pipe through it must enter and exit through exactly those two neighbours: the corner "elbow" is forced. Chain these: an elbow claims squares, which forces the next corner, and so on around the board.

2. Corridor fills

A one-square-wide corridor (between two drawn pipes, or a pipe and the wall) can only be traversed lengthwise. Whoever enters must run its full length — there's no room to turn. When a corridor forms, check who can possibly enter each end; if only one color can, that stretch of its pipe is decided. Deliberately creating corridors with a committed pipe is how strong players force the rest of the board.

3. Border chains

Walk the border as a sequence of squares. Each must be covered by some pipe, and border squares are covered either by a pipe running along the wall or by an elbow touching it. Between two dots that sit on the border, count the border squares: some color has to own that run, and usually only one candidate can reach both ends. This is the workhorse technique on hard boards — the border decides itself long before the middle does.

4. Pocket entrances

Any region of empty squares has a number of entrances (empty squares on its boundary adjacent to the outside). Count them:

• 0 entrances: the region is stranded — some earlier pipe is wrong.
• 1 entrance: only a pipe that ends inside (a dot in the pocket) can fill it. No dot inside → wrong.
• 2 entrances: one pipe must sweep in one door and out the other, covering everything — which usually determines the sweep's owner.

Pocket counting is the "X-ray" of flow: it converts a vague feeling of "this looks cramped" into a hard yes/no.

5. Dot-blocking

An endpoint dot is a wall to every other color — pipes can't pass through it. A dot sitting one square off a corner or in a narrow gap often seals a region for its own color alone. Before routing around a cluster of dots, note which passages they've already closed; harder boards hide their corridors this way.

6. The long-way principle, quantified

For each pair, compare the shortest possible connection with the area that will be left over if it takes it. All leftover area must be absorbed by other pipes — pipes can wiggle, but each covers one connected snake of squares. If the remaining pairs obviously can't stretch to absorb a region, the short route was wrong and the pipe you're holding must sweep that region itself. On expert boards, deciding which pipe absorbs which region is the entire game; the dots are sparse precisely so several assignments look plausible.

7. Sketch-and-cut

Not a deduction but a workflow: since drawing over a pipe cuts it and nothing is ever lost but time, use the board itself as scratch paper. Sketch the assignment you believe in, run the pocket counts on what remains, and cut the piece that fails. One honest sketch usually refutes or confirms a whole plan — far faster than staring.

Apply these in order — corners, corridors, border, pockets — and most hard boards fall without a single blind guess. For the attack order across a whole board, see the strategy guide.