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Magnum One (Mid-American Digital) (Disc Manufacturing).iso
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PEN2MINO.DOC
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1990-09-16
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P E N T O M I N O E S
The game of Pentominoes consists of 12 pieces, where each piece
consists of 5 squares (hence the name pento-mino). The pieces
are unique in shape and resemble letters of the alphabet so they
are named according to this scheme:
TTT U U V W X Y ZZ FF IIIII LLLL PP NN
T UUU V WW XXX YYYY Z FF L PP NNN
T VVV WW X ZZ F P
Together, all the pieces total 60 squares. The most amazing
thing about these pentominoes is that they can be fitted together
to form the following rectangles:
6 X 10, 5 X 12, 4 X 15 and even 3 X 20!
If you feel challenged, you may make pentominoes from cardboard
by carefully marking off reqularly spaced qrid lines and tracing
the various pieces, then cutting them. You might like to try
building just even one 6X10 rectangle!
Another popular shape that the pentominoes can fill is a an 8 X 8
square with a 2 X 2 hole in the middle. You can get several
symmetrical patterns from this board.
The triplication problem may be stated this way: Take a
pentomino, say "F". Without using the F-pentomino itself, it is
possible to use 9 of the remaining pentominoes to build a shape
which is 3 times as high and 3 times as wide as the selected
pentomino.
If you add a unit thickness to the 12 shapes, then you have a set
of solid pentominoes. And surprise, surprise! - they may be used
to build 3-dimensional bricks of these dimensions:
3 x 4 x 5 and 2 x 5 x 6 and 2 x 3 x 10
But I leave those problems for you! (Actually, I managed to come
up with a solid pentomino program but it took more than 2 hours
to even arrive at 1 solution to the 3 x 4 x 5 so I gave up!)
I hope you enjoy these programs.
Manny Juan
61 Oakmont Drive
Daly City, CA 94015