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).
-------------------------------------------------------------------------
A similar question appeard in: Puzzletopia No 101 (15th Aug. 1995).CONTEST
                                                                   =======
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.
-------------------------------------------------------------------------

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.
-------------------------------------------------------------------------
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.