Years ago, I programmed a polyomino solution engine, that was able to solve any polyomino puzzle, based on run-time 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 |
H-shaped. |
 |
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 Montgomery-Smith. |
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 one-sided pentominoes to construct a 3 x 30 rectangle. |
 |
46 |
|
|
- |
Use the one-sided pentominoes to construct a 5 x 18 rectangle. |
 |
686628 |
|
|
- |
Use the one-sided pentominoes to construct a 6 x 15 rectangle. |
 |
2567183 |
|
|
- |
Use the one-sided pentominoes to construct a 9 x 10 rectangle. |
 |
10440433 |
|
|
- |
A symmetrical shape, constructed from the set of one-sided 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 Wen-Shan 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 one-sided hexomino puzzles to my attention. |
Use the 60 one-sided hexominoes to make a 5 x 72 rectangle. |
 Solution provided by Stephen Montgomery-Smith. |
Unknown |
|
|
- |
Use the 60 one-sided hexominoes to make a 6 x 60 rectangle. |
 Solution provided by Stephen Montgomery-Smith. |
Unknown |
|
|
- |
Use the 60 one-sided hexominoes to make a 8 x 45 rectangle. |
 |
Unknown |
|
|
- |
Use the 60 one-sided hexominoes to make a 9 x 40 rectangle. |
 |
Unknown |
|
|
- |
Use the 60 one-sided hexominoes to make a 10 x 36 rectangle. |
 |
Unknown |
|
|
- |
Use the 60 one-sided hexominoes to make a 12 x 30 rectangle. |
 |
Unknown |
|
|
- |
Use the 60 one-sided hexominoes to make a 15 x 24 rectangle. |
 |
Unknown |
|
|
- |
Use the 60 one-sided hexominoes to make a 18 x 20 rectangle. |
 |
Unknown |