With compliments

Ton Tillemans  [Sent GIF]
-----------------------------------
Hi Ed,

I enjoyed your report on this year's PDC.  I'll be sure to bookmark the links 
you put in this week's article.

I am always amazed at what people manage to create, both by the ingeniousness 
of the design and the beauty of the workmanship.  I should just break down and
get a display case, and then I wouldn't feel guilty about buying puzzles.  :-)

I didn't make a copy of the 2 x 2 offset-squares puzzle, but I sketched some 
things on paper until a solution fell out for the 7 x 9.  For the 8 x 8, I had
to resort to moving colored blocks around on my desk.  (I have an old set of 
children's blocks that I painted as the 30 6-color cubes back in junior high. 
Most people who see them have no idea what they are.)

I called the pieces /, V, C, and J, vaguely representative of their shape.  
The following pictures will look best in a squarish sort of monospace font.

For the 7 x 9:

//VV...
//VV.VV
.//VVVV
.//VVCC
JJ//.CC
JJ//CC.
.JJ.CC.
.JJJJCC
...JJCC

And the 8 x 8:

...JJ.CC
.JJJJ.CC
.JJ//CC.
JJ.//CC.
JJVV//CC
VVVV//CC
VV.VV//.
...VV//.

Take care,
Susan Hoover
----------------------------------
A friend found the 8x8 in the pub last night.
I found the 7x9 when I got home,
and the 8x8 a couple of minutes later.

8x8:
   +--+--+--+--+
   |     |     |
   +     +     +  +--+--+
   |     |     |  |     |
+--+--+  +--+  +--+     +
|     |     |           |
+     +     +     +--+--+
|     |     |     |     |
+--+  +--+  +--+--+     +
   |     |     |  |     |
   +     +     +--+  +--+
   |     |     |     |
+--+  +--+--+--+     +
|     |  |           |
+     +  +     +--+--+
|     |  |     |
+--+--+  +--+--+

7x9:
   +--+--+--+--+     +--+--+
   |     |     |     |     |
   +     +     +--+--+     +
   |     |                 |
   +--+  +--+--+     +--+--+
      |     |  |     |     |
+--+--+     +--+--+--+     +
|           |     |  |     |
+     +--+--+     +--+  +--+
|     |           |     |
+--+--+     +--+--+     +
|           |           |
+     +--+--+     +--+--+
|     |     |     |
+--+--+     +--+--+


-- 
Roger Phillips  
-----------------------------------
I made a simple version in cardboard, which helped me
find these solutions:

  ___   ___       
 |   | |   |___   
 |_  |_|___    |  
   |   |   |_  |_ 
  _|  _|  _|_|   |
 |   |   |   |___|
 |___|  _|  _    |
   |   |   | |___|
   |___|___|      
		  
          ___ ___ 
      ___|   |   |
     |    ___|  _|
    _|  _|_|   |  
   |   |   |_  |_ 
   |_ _|  _|_|   |
     |   |   |___|
    _|  _|  _    |
   |   |   | |___|
   |___|___|      


Thanks again,

 Trygve Flathen

-------------------------------------
That is an interesting little puzzle in spite of just having four pieces.
 
Mike Kemper

-------------------------------------
  To get the 8 x 8 I had 10 stabs before I got it on
the eleventh, but having the 8 x 8 I got 7 x 9 on the
first try. 

Robert Reid

-----------------------------------------
My colleague has found a way to fit them onto
a cylinder with curved surface area of 60:

+--+--+                 +--+--+
|     |                 |     |
+     +  +--+--+--+--+  +     +
|     |  |     |     |  |     |
+--+  +--+     +     +--+--+  +--+
   |           |           |     |
   +     +--+--+--+--+     +     +
   |     |  |     |  |     |     |
   +--+--+--+     +--+--+  +--+  +--+
      |                 |     |     |
      +     +--+--+     +     +     +
      |     |     |     |     |     |
      +--+--+     +--+--+--+--+--+--+

-- 

No doubt the 6x11 arrangement:
+--+--+--+--+--+--+
|     |     |     |
+     +     +     +  +--+--+--+--+
|     |     |     |  |     |     |
+--+  +--+  +--+  +--+     +     +
   |     |     |           |     |
   +     +     +     +--+--+  +--+
   |     |     |     |  |     |
+--+  +--+--+  +--+--+--+     +
|     |     |     |           |
+     +     +     +     +--+--+
|     |     |     |     |
+--+--+     +--+--+--+--+

is too trivial to mention, and its area is a wasteful 66,
compared with the 8x8 = 64 and 7x9 = 63 solutions.

However, one of my colleagues found an arrangement
that fits inside a rectangle of area 60.8
(if I've done my calculations correctly).

16/sqrt(5) x 19/sqrt(5):
               +--+--+
               |     |
         +--+--+     +
         |     |     |
         +     +--+  +--+
         |     |  |     |
+--+--+--+  +--+--+     +
|     |     |           |
+     +     +     +--+--+--+
|     |     |     |  |     |
+--+  +--+  +--+--+--+     +
   |     |     |           |
   +     +     +     +--+--+
   |     |     |     |
   +--+  +--+--+  +--+
      |     |     |
      +     +     +
      |     |     |
      +--+--+--+--+

I don't know if this is minimal.

Note that by shifting the leftmost piece,
a symmetrical shape (including the holes) can be made:

               +--+--+
               |     |
         +--+--+     +
         |     |     |
         +     +--+  +--+
         |     |  |     |
      +--+  +--+--+     +
      |     |           |
+--+--+     +     +--+--+--+
|     |     |     |  |     |
+     +--+  +--+--+--+     +
|     |  |     |           |
+--+  +--+     +     +--+--+
   |     |     |     |
   +     +--+--+  +--+
   |     |  |     |
   +--+  +--+     +
      |     |     |
      +     +--+--+
      |     |
      +--+--+
Roger Phillips