A Dissection Puzzle: Torsten Sillke, 28.12.95
Cut the letter H (made of seven squares) into several pieces and
rearrange them to make a perfect square. How many pieces are
necessary?
H: +---+ +---+
| | | |
+---+---+---+
| | | |
+---+---+---+
| | | |
+---+ +---+
This is an old question of Wolfgang Schneider (Kubi-Games, NKC 215).
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A similar question appeard in: Puzzletopia No 101 (15th Aug. 1995).CONTEST
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Seven puzzle from Junk Kato.
This is the same question as above but for the letter 7.
7: +---+---+---+
| | | |
+---+---+---+
| | | |
+---+ +---+
| |
+---+
| |
+---+
If you could solve this problem (the Seven Puzzle) in Four pieces,
write Nob. The first solver will get 20000 Yen.
nob = Nob Yoshigahara = HFB01453@niftyserve.or.jp
In Dec. 1997 Dick Hess told me, that up to now
he didn't heard of a solution.
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Greg Frederickson,
"Dissections: Plane & Fancy",
Cambridge University Press, 1997
Please check the following URL for a more complete description:
http://www.cs.purdue.edu/homes/gnf/book.html
With the T-strip method Greg Frederickson can do both dissections
with six pieces. Can you do better.
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From: Greg Frederickson
To: Torsten Sillke
Subject: Re: square a heptomino
Date: Fri, 12 Dec 1997 11:05:31 -0500
There are very few lower bounds known, and they seem to be
for rather limited cases and/or results. For example:
1. an irregular triangle of area 1 to a square,
in terms of the length of the longest side. - by M.J. Cohn.
Geom. Dedicata 1975. Probably not tight. His upper bound
is not tight.
2. two unequal squares to one, at least 4 pieces if
the cuts are parallel to the sides. tight for two classes
of Pythagorean triples.
3. three unequal cubes to one, at least 8 pieces if
the cuts are parallel to the sides. tight for 3, 4, 5 :: 6,
1, 6, 8 :: 9
4. two unequal cubes to two different cubes, at least 9 pieces if
the cuts are parallel to the sides. tight for 9, 10 :: 12, 1
But for the myriad of other dissection problems, I know of
no lower bounds. David Paterson, in Australia, is thinking
about a search involving exhaustive enumeration for some
of the simpler dissection problems. I don't know how far
he has gotten with that approach.