Path Puzzle Strategies: Corners, Dead Ends and Parity
The deductions that solve one-line path puzzles like Trail and Zip. Corners, numbers in order, dead ends, chessboard parity, plus a full 5x5 solve.
Trail and path puzzle guides
One line through every square: strategies, walls, Hidato and Numbrix, and the maths behind it.
Hidato vs Numbrix vs Trail: Number Path Puzzles Compared
Hidato allows diagonal steps, Numbrix does not, and Trail numbers are checkpoints. Their origins, the rules side by side, and one 4x4 path solved three ways.
How to Play Trail: One Line Through Every Square
Trail's rules in full: one line from 1 to the highest number, through every square, in order, never crossing a wall. Plus a 5x5 puzzle solved move by move.
The Maths Behind One-Line Puzzles: Hamiltonian Paths
What a Hamiltonian path is, from Hamilton's Icosian game to Euler's bridges, why computers find it hard in general, and why a small puzzle grid stays friendly.
Walls in Trail: How Barriers Make the Path Easier to Find
Walls in path puzzles take away choices, and every lost choice is information. Corridors, forced turns, fences with gaps and a walled 5x5 solved step by step.