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Learn to solve Flow-style puzzles

Lessons that take you from the basic rules to the reasoning behind hard boards, each built on original puzzles with worked examples.

These lessons teach you to solve Flow-style puzzles by reasoning, so you never have to guess and undo. Each one explains a single idea, shows it on small original boards, and links to practice puzzles that need it.

Start with How to play. It covers the rules and the words the other lessons use, such as path end, tip and hole. Then work through your first puzzle, a 5×5 board solved one move at a time.

The technique lessons are best read in order, because each builds on the one before. They begin with forced moves and corner squeezes, which settle most of an easy board. Next come dead ends, bottlenecks and thinking a few moves ahead, the checks that rule moves out. After those are the uniqueness trick, checkerboard parity and a method for large boards.

The last group covers other board types: bridges, hexagonal grids, warps and shaped boards.

Every board in the lessons is original, and any board that claims a property has been checked by an exact solver.

Start here

How to play Flow-style puzzlesThe rules, the vocabulary used in every lesson, and the beginner mistakes to unlearn.Your first puzzle, step by stepA 5×5 board solved move by move, naming the technique behind each step.

Solving techniques

Forced movesThe one-open-side rule, chains of forced moves and the joining case.Edges and cornersThe squeeze rule, corners, wall cells next to a path, and when hugging the wall fails.Dead ends and stranded cellsThree shapes that make a cell unfillable, and how to scan for them after every move.Bottlenecks and cut-off colorsNarrow gaps, cut-off colors, boxed-in path tips, and how to count what has to pass through.Thinking ahead without guessingTest a move by following its forced consequences to a contradiction, without ever guessing.The uniqueness trickRule out moves that would give a puzzle a second solution, and know when the 2×2 rule is safe.Checkerboard parityShade the grid like a checkerboard, count the pairs, and catch impossible boards and dead positions.Strategy for large boardsWhere to start on a big board, how to split it into regions and when to stop scanning and think ahead.

Other kinds of board

BridgesHow a bridge cell's two lanes change forced moves, bottlenecks and crossing pairs.Hexagonal boardsHow six neighbors per cell change corners, edges and forced moves, with a worked hex board.Warps and wrap-around boardsHow warps and wrap-around edges remove corners and edges, and what to use as anchors instead.Shaped boards and holesHow holes and irregular outlines create new corners and bottlenecks, plus a look at rings, cubes and linked loops.

Put it into practice

Every puzzle has hints and a walkthrough that names the technique behind each step.

#20 Knife Ridge12 × 12 · Expert #19 Talus12 × 12 · Advanced #18 Cat's Cradle11 × 11 · Expert #17 Bowline8 × 8 · Expert