Rectangles

• 3x20: 2 solutions

  

• 4x15: 368 solutions

  

• 5x12: 1010 solutions

  

• 6x10: 2339 solutions

  

Skewed Rectangles

• 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

  

Misc

• 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:

  188 solutions	21 solutions
  126 solutions	74 solutions

• 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:

  101 solutions

  82 solutions

• Crosses:

  14 solutions. Also see Pentominoes Plus the Monomino, cross 1.	84 solutions (design by Dan Klarskov)
  28 solutions (design by Dan Klarskov)	21 solutions
  4 solutions	164 solutions

• 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)
  1595 solutions

• “The Eye”: 1 solution (design by Joel Enwald)

  

• Arches:

  602 solutions	125 solutions
  85 solutions

• 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

  

Rectangles

• 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.