Bob Henderson mails us:"I found other classifications that depend on the letter of the alphabet each pentomino resembles, but I think that the geometric categories are less arbitrary."
He had the same idea as Martin Watson.

 

Tom Jolly USA

1 Does the piece have line symmetry? Image 2 Can it be placed flat on a table so that exactly 3 cubes touch the table? Image 3 Can you draw a line on it connecting all the cubes without backtracking? Image 4 Can you add or subtract 1 cube to turn the piece into a rectangle? Image

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L

N

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1

N

Y

N

N

N

Y

Y

Y

Y

Y

N

N

2

N

N

N

Y

Y

Y

Y

Y

N

N

N

N

3

N

Y

Y

Y

Y

N

Y

Y

Y

N

N

Y

4

N

Y

Y

N

Y

N

Y

N

N

N

Y

N

 

E. Künzell Germany

1   Can you construct the pentomino out of a domino and the triomino in the shape of a rectangle (3 sqares in a row)? Image 2     Is it possible to construct the 3x3 sqare and the tenth sqare added at one corner with the given one and another second pentomino? ( The task is similar to the one in the 4th question, but the shape is not like a house, but rather like a lorry)?    Image 3   Double the size of the pentomino by using 4 different pentominoes. Are there more than 2 different solutions? Image 4   Can this pentomino together with another pentomino make the following decamino?    Image

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N

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1

N

Y

Y

Y

Y

Y

N

Y

N

N

N

N

2

Y

N

Y

N

Y

Y

Y

Y

N

N

Y

Y

3

N

N

Y

Y

Y

N

Y

N

Y

N

N

Y

4

Y

N

N

Y

Y

N

Y

Y

N

Y

N

N

 

Helmut Postl Austrich

1   Can this pentomino together with another pentomino be used to cover the following shape?    Image   2 Does the pentomino fit into a 2x5-rectangle? Image 3 Does the pentomino contain a T-tetromino? Image 4 : Does the pentomino have exactly 8 edges? Image

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N

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1

Y

N

Y

N

Y

Y

Y

Y

N

N

Y

Y

2

N

Y

Y

Y

Y

N

Y

N

N

N

Y

N

3

Y

N

N

N

Y

Y

N

N

N

Y

Y

N

4

N

N

N

Y

N

Y

Y

N

N

N

Y

Y

 

Jaap Scherphuis

1 Does it have line symmetry? Image 2   Does it fit inside this figure (a 3x3 square with a 1x2 corner missing)?      x      xxx      xxx Image 3   Count the number of squares with exactly two neighbouring squares, on opposing sides. Is this an odd number? Image 4   Count the number of squares with exactly two neighbouring squares, on non-opposing sides. Are there at least two such squares?  Image

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1

N

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N

N

N

Y

Y

Y

Y

Y

N

N

2

Y

N

N

N

Y

Y

Y

Y

Y

N

N

Y

3

N

Y

N

Y

N

Y

Y

N

N

N

Y

Y

4

N

N

N

Y

Y

N

Y

N

Y

N

N

Y

 

Peter Sipos (Hongarije)

1 Does it have line symmetry? Image 2 Is the adjacency graph of the constituting squares a path (node degrees < 3)? Image 3 Is the area of the bounding rectangle less than 9? Image 4   Can the following decamino be solved using this pentomino?    Image

F

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N

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1

N

Y

N

N

N

Y

Y

Y

Y

Y

N

N

2

N

Y

Y

Y

N

N

Y

Y

Y

N

N

Y

3

N

Y

Y

Y

Y

N

Y

N

N

N

Y

N

4

Y

N

N

Y

Y

N

Y

Y

N

Y

N

N

 

Aad v. d. Wetering

1 Do you have line symmetry? Image 2 Do you fit inside a 3x3 square, touching all sides? Image 3 Are the numbers of your squares' individual outer edges - sorted - 2-2-2-3-3? Image 4   Do two copies fit inside a 2x5 rectangle and/or inside the figure shown below?       X       XXXX       XXXX              X Image

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Y

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1

N

Y

N

N

N

Y

Y

Y

Y

Y

N

N

2

Y

N

N

N

N

Y

N

Y

Y

Y

N

Y

3

N

Y

Y

Y

N

N

Y

Y

Y

N

N

Y

4

N

Y

Y

N

Y

Y

N

Y

N

N

N

N

With these 15 questions there are 1365 different possible combinations of 4 questions, of which only 29 different combinations each uniquely determine the pentominoes:

1-2-3-4	1-2-3-6	1-2-3-7
1-2-3-9	1-2-3-11	1-2-3-13
1-2-4-5	1-2-5-14	1-2-5-15
1-2-6-15	1-2-7-14	1-2-9-15
1-2-11-14	1-2-13-14	1-3-6-8
1-3-6-15	1-3-7-14	1-3-8-9
1-3-9-15	1-3-11-14	1-3-13-14
1-5-8-14	3-5-6-14	3-5-6-15
3-5-9-14	3-5-9-15	3-5-10-14
3-5-10-15	3-5-12-14

J. Viljoen mails us:"Herewith my lazy solution.Yes, I know it is cheating. Or is it? It seems to meet the specifications of the challenge, at least the way I read them."
Alphabetise the pentominoes as is the custom: F I L N P T U V W X Y Z. Now, using this alphabetical order, number them from 1 to 12. F will therefore be 1, and Z will be 12. Turn this number into a 4-bit binary number.
 

J. Viljoen South-Africa

1 Is the first bit set (ie equal to 1)?   2 Is the second bit set (ie equal to 1)?   3 Is the third bit set (ie equal to 1)?   4 Is the fourth bit set (ie equal to 1)?

F :0001

I:0010

L:0011

N:0100

P:0101

T:0110

U:0111

V:1000

W:1001

X:1010

Y:1011

Z:1100

1

Y

N

Y

N

Y

N

Y

N

Y

N

Y

N

2

N

Y

Y

N

N

Y

Y

N

N

Y

Y

N

3

N

N

N

Y

Y

Y

Y

N

N

N

N

Y

4

N

N

N

N

N

N

N

Y

Y

Y

Y

Y

 

M.H. Watson England

1  Is this pentomino V,W,X,Y or Z?   2  Is this pentomino N,P,T,U or Z? 3  Is this pentomino I,L,T,U,X or Y?   4  Is this pentomino F,L,P,U,W or Y?

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1

N

N

N

N

N

N

N

Y

Y

Y

Y

Y

2

N

N

N

Y

Y

Y

Y

N

N

N

N

Y

3

N

Y

Y

N

N

Y

Y

N

N

Y

Y

N

4

Y

N

Y

N

Y

N

Y

N

Y

N

Y

N

Martin mails us: "This probably isn’t the kind of answer you wanted, but I like it. I am sure your class will enjoy it!!
This is effectively allocating each pentomino a binary number from F=0001 upto Z=1100. Each ‘1’ corresponds with a YES.
Every pentomino has a different answer. This would still work if there were 16 pentominoes, from 0000 to 1111."
We have nothing to add to this.

If you find any error or incompleteness, please mail to: