Re: Divide a shape into four equal parts

On Tue, 1 Jul 2025 19:01:29 -0000 (UTC), Richard Tobin wrote:

A well-known puzzle is to divide an L-shape - a square with one square
quarter removed - into four identical pieces.

I haven't attempted your original question yet, but for anyone who has.
Henry Ernest Dudeney had a variation of that first puzzle in "Amusements
in Mathematics". He also has a variation on the puzzle with the square,
with a triangle removed. More on that later. Here's the first variation...

180. THE FOUR SONS

Readers will recognize the diagram as a familiar friend of their youth. A
man possessed a square shaped-estate. He bequeathed to his widow the
quarter of it that is shaded off. The remainder was to be divided
equitably amongst his four sons, so that each should receive land of
exactly the same area and exactly similar in shape. We are shown how this
was done. But the remainder of the story is not so generally known. In the
centre of the estate was a well, indicated by the dark spot, and benjamin,
Charles and David complained that the division was not "equitable," since
Alfred had access to this well, while they could not reach it without
trespassing on somebody else's land.The puzzle is to show how the estate
is to be apportioned so that each son shall have land of the same shape
and area, and each have access to the well without going off his own land.

The accompanying image is available here:

http://www.puzzles.50webs.org/pics/q180.png

Most of the puzzles from Dudeney's book are available here:

http://www.puzzles.50webs.org/index.html

--
David Entwistle