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