Author: | David Goodger <goodger@python.org> |
---|---|
Date: | 2016-12-04 |
Revision: | 640 |
Web site: | http://puzzler.sourceforge.net/ |
Copyright: | © 1998-2016 by David J. Goodger |
License: | GPL 2 |
Contents
3x20: 2 solutions
4x15: 368 solutions
5x12: 1010 solutions
6x10: 2339 solutions
20x3: 2 solutions
These are the same two solutions as the 3x20 rectangle above, just cut at the W pentomino and rearranged.
15x4: 138 solutions
12x5: 233 solutions
This solution can be easily rearranged into a solution to the 5x12 rectangle above, but not all solutions share this property.
10x6: 156 solutions
3x20 ring (3x20 rectangle joined at the ends): 2 solutions (same as the 3x20 rectangle; the V piece forces a partition)
3x20 tube (3x20 rectangle joined at the long edges): 48,928 solutions (at least, depending on how pieces that wrap around on themselves are defined)
8x8 square with a central 2x2 hole: 65 solutions
8x8 square with missing corners: 2170 solutions
8x8 squares with four holes:
3x21 rectangle with holes: 6 solutions (an example puzzle from How to Extend Polyform Puzzler)
10x10 triangle with one omitted piece: 580 solutions
Solutions are possible omitting all but the "P" & "W" pieces. This solution omits the "V" piece (shown to the side):
15x8 triangle: 8 solutions
Truncated triangle: 3626 solutions
11x10 diamond: 8 solutions
(The configuration with a central hole has no solutions, unfortunately. But see the diamond puzzle in Pentominoes Plus the Monomino.)
Trapezoid: 140 solutions
Chevrons:
Crosses:
14 solutions. Also see Pentominoes Plus the Monomino, cross 1. |
84 solutions (design by Dan Klarskov) |
28 solutions (design by Dan Klarskov) |
|
Flowers:
47 solutions (design by Dan Klarskov) |
414 solutions (design by Dan Klarskov) |
15 solutions (design by Dan Klarskov) |
57 solutions (design by Dan Klarskov) |
“The Eye”: 1 solution (design by Joel Enwald)
Arches:
Yin-Yang: 3 solutions
Holey oval: 2 solutions
Spinner (design from Thimo Rosenkranz's pentoma.de): 13 solutions
Holey spinner (design from John Greening): 3 solutions
8x8 square: 16146 solutions
The 8x8 square with a central 2x2 hole puzzle above can be considered a subset of this puzzle.
15x8 triangle: 473 solutions
Crosses
5380 solutions (design by Dan Klarskov) |
2071 solutions (design by Dan Klarskov) |
177 solutions (design by Dan Klarskov) |
2 solutions (design by Dan Klarskov) |
Diamond: 22 solutions
(The symmetrical configuration with a central hole has no solutions, unfortunately.)
Cross 1 (suggested by Dan Klarskov): 366 solutions
Diamond: 10 solutions
In all solutions the monomino is at the edge of the diamond.
These are just like regular pentominoes, except that non-isomorphic reflections (different shape when flipped over) are treated as separate pieces, and pieces are not allowed to be flipped.
3x30: 46 solutions
5x18: 686,628 solutions (incomplete list)
6x15: 2,567,183 solutions (incomplete list)
9x10: 10,440,433 solutions (incomplete list)
10,440,433 solutions (non-isomorphic in reflection, reflections allowed when counting solutions) are reported in "One-sided Pentominoes in a 9 x 10 Rectangle" by Alfred Wassermann, University of Bayreuth, 2000.
The numbers of solutions for the last three puzzles above were taken from Gerard Putter's Polyomino Solution Page, as reported by Stephen Montgomery-Smith.