Author: | David Goodger <goodger@python.org> |
---|---|

Date: | 2013-05-24 |

Revision: | 580 |

Web site: | http://puzzler.sourceforge.net/ |

Copyright: | © 1998-2012 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)

Arches:

Yin-Yang: 3 solutions

Holey oval: 2 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.