THE KNIGHT’S TOUR

how to take a knight over all 64 squares without landing on any twice: Warnsdorff’s rule and what to do with ties

Built as a memo rather than a table: the thing worth hanging it up for reads across the room, with the full reference in smaller type below it.

Three sizes in one archive — from a sheet on the fridge to a poster on the wall.

Formats: A4 · A3 · A2
What you get: Print-ready PDFs, one per size, with every letterform converted to outlines — nothing to install, nothing to shift.
Subject: maths · everyone · memo · classroom

A knight jumps two squares one way and one square to the side. A tour is a path that visits every square of the board exactly once. Files a–h, ranks 1–8 from the bottom, as in chess.

ON A 5 × 5 BOARD THE TOUR NEVER CLOSES

A tour is closed if the knight can jump from its last square back to the first. A chessboard has 26,534,728,821,064 closed tours, counting each direction separately but not the starting square (B. McKay, 1997). A 5 × 5 board has 1,728 tours and not one of them is closed. Every jump changes the colour of the square. 25 squares take 24 jumps, so the last square has the colour of the first, and from it the knight can only jump to the other colour. The same holds on every board with an odd number of squares.

On the sheet

A knight jumps two squares one way and one square to the side. A tour is a path that visits every square of the board exactly once. Files a–h, ranks 1–8 from the bottom, as in chess.
Colour carries meaning, but meaning never rests on colour alone — the sheet reads in black and white.
Nothing about how it was made: the sheet carries only what the reader needs.

Printing

Three sizes in the archive: A4 — 210×297 mm, A3 — 297×420 mm, A2 — 420×594 mm.
All text is converted to outlines. No fonts to install, and nothing shifts on another machine.
White background and sparing fills — it prints on a home printer without draining the cartridge.
Margins of at least 10 mm: a home printer cannot print to the edge.
No stroke thinner than 0.3 mm, so nothing disappears in print.

Why the numbers can be trusted. Every countable number here is computed from data rather than typed in, and the sheet must pass 5 independent checks before it is allowed to build — how many items there are, the order they come in, and the claim in the highlighted box itself. If one fails, there is no file.

THE KNIGHT’S TOUR

ON A 5 × 5 BOARD THE TOUR NEVER CLOSES

On the sheet

Printing

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