Skinjo and the Haberdasher’s Problem: Four Pieces, Unsettled Credit

The square closes. The credit does not.

Morning light catches the cut edges as Skinjo divides an equilateral triangle of card into four pieces. The first rearrangement is slow: slide, turn, stop before the corners collide. Then the pieces settle into a square. Back they go, until the triangle returns. Nothing has been added; the outline has simply changed its mind.

A second, matching set lets the two arrangements sit side by side on the worktable. Skinjo nudges a seam flush with a fingertip. The card has begun to show the handling. This is a painter’s kind of looking: the same material, a different boundary, and the eye briefly unwilling to believe the area stayed put.

The printed history takes three turns of its own. On 6 April 1902, Henry Dudeney posed the problem in his column: dissect an equilateral triangle so its pieces can be rearranged into a square of equal area, using as few pieces as possible. On 20 April, he supplied a five-piece solution while reporting that C. W. McElroy of Manchester had found one using four. On 4 May, Dudeney presented the four-piece solution.

That sequence matters. It records McElroy’s reported success before the four-piece construction appeared, but it does not settle whether the dissection should be credited to McElroy or Dudeney. A familiar name attached to a puzzle is not, by itself, a receipt for its invention.

The haberdasher arrived in the storytelling: a fictional challenger asking the Canterbury pilgrims to turn a triangle of cloth into a square with four pieces. That tale appeared in The London Magazine in 1903 and was collected in 1907. Cloth supplied the name; card makes a useful rehearsal.

Skinjo turns the square back into a triangle once more. The seams meet neatly. The attribution remains an open edge.

Historical source: Wolfram MathWorld, “Haberdasher’s Problem” — https://mathworld.wolfram.com/HaberdashersProblem.html