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Pentomino Solutions to Rectangular Boards
3 X 20 2
4 X 15 368
5 X 12 1010
6 X 10 2339
Number of Possible Arrangements
Type Puzzle 1-Sided All Pieces
Pieces Ways w/ holes
1 1 1 1
2 1 1 2
3 2 2 6
4 5 7 19
5 12 18 63
6 35 60 216
7 108 196 760 1
8 369 704 2725 6
9 1285 2500 9910 37
10 4655 9189 36446 195
11 17073 33896 135268 979
12 63600 126759 505861 4663
13 238591 476270 1903890 21474
14 901971 1802312 7204874 96496
15 3426576 6849777 27394666 425365
16 13079255 26152418 104592937
17 50107909 100203194 400795844
18 192622052 385221143 1540820542
19 742624232
20 2870671950
21 11123060678
22 43191857688
23 168047007728
24 654999700403
Puzzle Pieces = Different arrangements if rotation and reflection don't count.
1-Sided = Counts as different if reflection (flip-over) looks different.
All Ways = Counts as different if rotation or reflection looks different.
Puzzle pieces includes pieces with holes. (363 octominoes w/o and 6 w/ holes)
Polyomino Puzzle Pieces
1 Domino
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2 Trominoes
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5 Tetrominoes
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12 Pentominoes
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35 Hexominoes
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108 Heptominoes
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hole
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