THE FIFTEEN PUZZLE

how to solve any solvable position: the order, the last two tiles of a row, and how to tell whether a solution exists

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 move slides one tile next to the empty square into it. Solved means 1 to 15 in order, row by row, with the empty square in the bottom right corner.

14 AND 15 FOR $1,000

Sam Loyd claimed to have offered $1,000 to anyone who could put the swapped 14 and 15 back in order. It could never be won: in 1879 Johnson and Story proved that half of all arrangements cannot be solved, and this is one of them. Nor was the puzzle Loyd’s: it is credited to a postmaster, Noyes Chapman, and in 1880 it became a craze across the United States.

On the sheet

A move slides one tile next to the empty square into it. Solved means 1 to 15 in order, row by row, with the empty square in the bottom right corner.
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 11 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 FIFTEEN PUZZLE

14 AND 15 FOR $1,000

On the sheet

Printing

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