Years ago, I programmed a polyomino solution engine, that was able to solve any polyomino puzzle, based on runtime parameters. The first version of this program was written in Pascal, for the Apple II computer, and later I converted it to ANSI C, so it could be compiled for (almost) any computer. The same program is now avaliable in Java. On this page are a number of examples. In all puzzles exactly the same java applet is used; the different puzzles are completely specified in HTML.
Most of the problems presented on this page are published in Appendix B of Solomon Golomb's book. I left out two kinds of problems: those my applet cannot solve, and those for which has been proven no solutions exist. Each problem is presented with its number from the appendix in Golomb's book, a short description, a tiny picture of a solution, and the total number of solutions according to the applet. I added some problems myself, which don't have a number. Clicking the "Solve" link starts the solver in a separate window.
No. 
Description 
Example 
Solutions 


1 
Fit the 12 pentominoes into one 3 x 20 rectangle. 

2 

2 
Fit the 12 pentominoes into one 4 x 15 rectangle. 

368 

3 
Fit the 12 pentominoes into one 5 x 12 rectangle. 

1010 

4 
Fit the 12 pentominoes into one 6 x 10 rectangle. 

2339 

5 
This shape consists of two congruent subparts. 

1 

6 
This shape consists of two congruent subparts. 

23 

7 
This shape consists of two congruent subparts. 

37 

8 
One of the subparts is a triangle (congruent subparts are not possible here). 

36 

9 
An 8 x 8 with the corners removed, and consisting of two congruent subparts. 

16 

 
All solutions for an 8 x 8 with the corners removed. 

2170 

10 
An 8 x 8 with four holes. 

21 

11 
An 8 x 8 with four holes. 

188 

12 
An 8 x 8 with a hole in the middle, and consisting of two congruent subparts. 

12 

 
All solutions for an 8 x 8 with a hole in the middle. 

65 

13 
An 8 x 8 with four holes. 

64 

14 
Yet another 8 x 8 with four holes. 

126 

 
Yet even more 8 x 8 with four holes. 

74 

 
An 8 x 8 with a 2 x 2 corner missing. 

5027 

 
An 8 x 8 with 12 pentominoes and one 2 x 2 tetromino. 

16146 

15 
3 x 21 with three squares missing. 

6 

16 
8 x 9 with a 3 x 4 hole. 

9 

17 
Rectangle with four protrusions. 

841 

18 
Hshaped. 

377 

19 
A cross. 

14 

21 
Jagged square with 12 pentominoes and one monomino. The monomino can only be at the edge. 

10 

22 
Two parts form either a 8 x 8 or a 9 x 7. 

1 

23 
Weird shape, which can be folded to cover a cube. 

3 

24 
The 5 x 12 rectangle contains a 5 x 5 subpart. 

16 

25 
2 rectangles of 5 x 6 each. 

16 

28 
Two congruent parts can form a 6 x 10 or a 9 x 7 rectangle. 

5 

29 
Two congruent parts can form a 6 x 10 or a 9 x 7 rectangle. 

10 

37.1 
Triplication of the "F": use 9 of the other pentominoes to construct an "F" three times the normal size. 

125 

37.2 
Triplication of the "I". 

19 

37.3 
Triplication of the "L". 

113 

37.4 
Triplication of the "N". 

68 

37.5 
Triplication of the "P". 

497 

37.6 
Triplication of the "T". 

106 

37.7 
Triplication of the "U". 

48 

37.8 
Triplication of the "V". 

63 

37.9 
Triplication of the "W". 

91 

37.10 
Triplication of the "X". 

15 

37.11 
Triplication of the "Y". 

86 

37.12 
Triplication of the "Z". 

131 

58 
Construct an 8 x 10 rectangle from the 12 pentominoes and the 5 tetrominoes. 

3386001688 

59 
Construct an 4 x 20 rectangle from the 12 pentominoes and the 5 tetrominoes. 

88501957 

60 
Obtain simultaneous solutions for the previous two problems by constructing two 4 x 10 rectangles. 

447768 

61 
Construct a 5 x 16 rectangle from the 12 pentominoes and the 5 tetrominoes. 

523899709 

 
Use the set of 35 hexominoes to construct this almost rectangular shape. It is not possible to fit the hexominoes into a perfect rectangle. 

Unknown 

62 
Use the set of 35 hexominoes to construct a parallelogram 

Unknown 

63 
Use the set of 35 hexominoes to construct a rectangle with a cross. 

Unknown 

64 
Use the set of 35 hexominoes to construct this shape. 
Solution provided by Andrew Clarke 
Unknown 

65 
Use the set of 35 hexominoes to construct this shape. 
Solution provided by Stephen MontgomerySmith. 
Unknown 

66 
Use the set of 35 hexominoes to construct this knight. 
This solution by Andrew Clarke 
Unknown 

67 
Use the set of 35 hexominoes to construct this rook. 

Unknown 

68a 
Use the 35 hexominoes and the 12 pentominoes to build a 18 x 15 rectangle. 

Unknown 

68b 
Like 68a, but now the pentominoes form a "rook" in the center of the rectangle. I had to split it into two puzzle definitions; puzzle 1 is the hexomino part, puzzle 2 the pentomino part. 

1: Unknown 2: 19 Total: Unknown 

82 
Use the 12 pentominoes to construct this shape. 

2 

83 
Use the 12 pentominoes to construct this shape. 

25 

85 
Build simultaneous 3 x 5 and 5 x 9 rectangles from the 12 pentominoes. 

8 

86 
Build simultaneous 4 x 5 and 4 x 10 rectangles from the 12 pentominoes. 

40 

89 
Use the 12 pentominoes to construct this cross. 

21 

90 
Use the 12 pentominoes to construct this cross. 

14 

 
Use the onesided pentominoes to construct a 3 x 30 rectangle. 

46 

 
Use the onesided pentominoes to construct a 5 x 18 rectangle. 

686628 

 
Use the onesided pentominoes to construct a 6 x 15 rectangle. 

2567183 

 
Use the onesided pentominoes to construct a 9 x 10 rectangle. 

10440433 

 
A symmetrical shape, constructed from the set of onesided tetrominoes. 

1 

 
Fill this shape using the 108 heptominoes. Special thanks to Steve Strickland for defining the
heptomino set. 

Unknown 

 
Create three congruent rectangles with a hole, using the 108 heptominoes. 

Unknown 

Thanks to WenShan Kao for bringing this "13 holes problem" to my attention. 
Use the 12 pentominoes to fill this shape full of holes. 

2 

Thanks to Andrew Clarke for bringing the onesided hexomino puzzles to my attention. 
Use the 60 onesided hexominoes to make a 5 x 72 rectangle. 
Solution provided by Stephen MontgomerySmith. 
Unknown 

 
Use the 60 onesided hexominoes to make a 6 x 60 rectangle. 
Solution provided by Stephen MontgomerySmith. 
Unknown 

 
Use the 60 onesided hexominoes to make a 8 x 45 rectangle. 

Unknown 

 
Use the 60 onesided hexominoes to make a 9 x 40 rectangle. 

Unknown 

 
Use the 60 onesided hexominoes to make a 10 x 36 rectangle. 

Unknown 

 
Use the 60 onesided hexominoes to make a 12 x 30 rectangle. 

Unknown 

 
Use the 60 onesided hexominoes to make a 15 x 24 rectangle. 

Unknown 

 
Use the 60 onesided hexominoes to make a 18 x 20 rectangle. 

Unknown 