Gerard's Universal Polyomino Solver



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

Solve

1

Fit the 12 pentominoes into one 3 x 20 rectangle.

2

Solve

2

Fit the 12 pentominoes into one 4 x 15 rectangle.

368

Solve

3

Fit the 12 pentominoes into one 5 x 12 rectangle.

1010

Solve

4

Fit the 12 pentominoes into one 6 x 10 rectangle.

2339

Solve

5

This shape consists of two congruent subparts.

1

Solve

6

This shape consists of two congruent subparts.

23

Solve

7

This shape consists of two congruent subparts.

37

Solve

8

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

36

Solve

9

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

16

Solve

-

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

2170

Solve

10

An 8 x 8 with four holes.

21

Solve

11

An 8 x 8 with four holes.

188

Solve

12

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

12

Solve

-

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

65

Solve

13

An 8 x 8 with four holes.

64

Solve

14

Yet another 8 x 8 with four holes.

126

Solve

-

Yet even more 8 x 8 with four holes.

74

Solve

-

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

5027

Solve

-

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

16146

Solve

15

3 x 21 with three squares missing.

6

Solve

16

8 x 9 with a 3 x 4 hole.

9

Solve

17

Rectangle with four protrusions.

841

Solve

18

H-shaped.

377

Solve

19

A cross.

14

Solve

21

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

10

Solve

22

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

1

Solve

23

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

3

Solve

24

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

16

Solve

25

2 rectangles of 5 x 6 each.

16

Solve

28

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

5

Solve

29

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

10

Solve

37.1

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

125

Solve

37.2

Triplication of the "I".

19

Solve

37.3

Triplication of the "L".

113

Solve

37.4

Triplication of the "N".

68

Solve

37.5

Triplication of the "P".

497

Solve

37.6

Triplication of the "T".

106

Solve

37.7

Triplication of the "U".

48

Solve

37.8

Triplication of the "V".

63

Solve

37.9

Triplication of the "W".

91

Solve

37.10

Triplication of the "X".

15

Solve

37.11

Triplication of the "Y".

86

Solve

37.12

Triplication of the "Z".

131

Solve

58

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

3386001688
(Stephen Montgomery-Smith)

Solve

59

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

88501957
(Stephen Montgomery-Smith)

Solve

60

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

447768

Solve

61

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

523899709
(Stephen Montgomery-Smith)

Solve

-

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

Solve

62

Use the set of 35 hexominoes to construct a parallelogram

Unknown

Solve

63

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

Unknown

Solve

64

Use the set of 35 hexominoes to construct this shape.


Solution provided by Andrew Clarke

Unknown

Solve

65

Use the set of 35 hexominoes to construct this shape.


Solution provided by Stephen Montgomery-Smith.

Unknown

Solve

66

Use the set of 35 hexominoes to construct this knight.


This solution by Andrew Clarke

Unknown

Solve

67

Use the set of 35 hexominoes to construct this rook.

Unknown

Solve

68a

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

Unknown

Solve 1

Solve 2

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

Solve

82

Use the 12 pentominoes to construct this shape.

2

Solve

83

Use the 12 pentominoes to construct this shape.

25

Solve

85

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

8

Solve

86

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

40

Solve

89

Use the 12 pentominoes to construct this cross.

21

Solve

90

Use the 12 pentominoes to construct this cross.

14

Solve

-

Use the one-sided pentominoes to construct a 3 x 30 rectangle.

46

Solve

-

Use the one-sided pentominoes to construct a 5 x 18 rectangle.

686628
(Stephen Montgomery-Smith)

Solve

-

Use the one-sided pentominoes to construct a 6 x 15 rectangle.

2567183
(Stephen Montgomery-Smith)

Solve

-

Use the one-sided pentominoes to construct a 9 x 10 rectangle.

10440433
(Stephen Montgomery-Smith)

Solve

-

A symmetrical shape, constructed from the set of one-sided tetrominoes.

1

Solve

-

Fill this shape using the 108 heptominoes.

Special thanks to Steve Strickland for defining the heptomino set.
Check out Steve's excellent puzzle site at http://www.stevespuzzleshop.com

Unknown

Solve

-

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

Unknown

Solve

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

Solve

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

Solve

-

Use the 60 one-sided hexominoes to make a 6 x 60 rectangle.


Solution provided by Stephen Montgomery-Smith.

Unknown

Solve

-

Use the 60 one-sided hexominoes to make a 8 x 45 rectangle.

Unknown

Solve

-

Use the 60 one-sided hexominoes to make a 9 x 40 rectangle.

Unknown

Solve

-

Use the 60 one-sided hexominoes to make a 10 x 36 rectangle.

Unknown

Solve

-

Use the 60 one-sided hexominoes to make a 12 x 30 rectangle.

Unknown

Solve

-

Use the 60 one-sided hexominoes to make a 15 x 24 rectangle.

Unknown

Solve

-

Use the 60 one-sided hexominoes to make a 18 x 20 rectangle.

Unknown


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