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From: David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz>
Newsgroups: rec.puzzles
Subject: Re: Divide a shape into four equal parts
Date: Sat, 5 Jul 2025 07:47:26 -0000 (UTC)
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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