Records Challenge 23 
 

Gabriele Carelli
G. Carelli
Italy

1

 

Is this pentomino flippable?
I'm not sure that "flippable" it's an English word, I hope you can undestand the meaning, if not let me know.

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2

It's possible to cover this pentomino with a domino and a I trimino?

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3

It's possible to cover this pentomino with a T-tetromino and a single square?

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4

It's possible to move a single square to reach the W-pentomino?

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F I L N P T U V W X Y Z

1

N Y N N N Y Y Y Y Y N N

2

N Y Y Y Y Y N Y N N N N

3

Y N N N Y Y N N N Y Y N

4

Y N N Y Y N N Y Y N N Y

 

Jeroen De Vos
Jeroen De Vos
Belgium

1

Is the piece symmetric to an axis?

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2

Is the number of 90° angles 6 or 7?

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3

Is it the net of an open box and  doesn't contains a S-tetromino?

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4
 

Can you construct the pentomino out of a  I-tromino and 2 monomino's, but the pentomino mustn't contain a I-tetromino or a  T-tetromino?

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F I L N P T U V W X Y Z

1

N Y N N N Y Y Y Y Y N N

2

Y N N Y N Y Y N Y N Y Y

3

N N Y N N Y N N N Y Y Y

4

N N N Y N N Y Y N N N Y

 

Peter Esser
Peter Esser
Germany

1

Is the piece a combination of the domino and the straight tromino?

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2

Is the piece symmetric to an axis?

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3

Has the piece exactly two ends i.e. two squares with only one connection?

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4

Is the number of inner corners (270° angles) odd?

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F I L N P T U V W X Y Z

1

N Y Y Y Y Y N Y N N N N

2

N Y N N N Y Y Y Y Y N N

3

N Y Y Y N N Y Y Y N N Y

4

Y N Y N Y N N Y Y N N N

 

Bob Henderson
B. Henderson
USA

1

Any Symmetry (across line and/or point) ?

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2

Contains L tetromino but not I tetromino?

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3

Has some ends pointed 90 degees apart?

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4

Has some ends pointed 180 degrees apart?

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5

Line symmetry?

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6

Contains L tetromino but not N tetromino?

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Each scheme uses the relative directions of the pentomino ends in 2 of the 4 classification criteria, so I should explain that these "ends" and their "directions" are the same as in Martin Watson's recent Pentomino Pipes challenge.

 

F I L N P T U V W X Y Z

1

N Y N N N Y Y Y Y Y N Y

2

Y N N Y Y Y Y Y N N N Y

3

Y N Y N N Y N Y Y Y Y N

4

Y Y N N Y Y N N N Y Y Y

 

F I L N P T U V W X Y Z

3

Y N Y N N Y N Y Y Y Y N

4

Y Y N N Y Y N N N Y Y Y

5

N Y N N N Y Y Y Y Y N N

6

N N Y N N Y Y Y N N Y Y

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
Tom Jolly
USA

1

Does the piece have line symmetry?

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2

Can it be placed flat on a table so that exactly 3 cubes touch the table?

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3

Can you draw a line on it connecting all the cubes without backtracking?

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4

Can you add or subtract 1 cube to turn the piece into a rectangle?

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F I L N P T U V W X Y Z

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

 

Ekkehard Künzell
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)?

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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)?
  

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3
 

Double the size of the pentomino by using 4 different pentominoes. Are there more than 2 different solutions?

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4

 

Can this pentomino together with another pentomino make the following decamino?
  

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F I L N P T U V W X Y Z

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
Helmut Postl
Austrich

1

 

Can this pentomino together with another pentomino be used to cover the following shape?
  

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2

Does the pentomino fit into a 2x5-rectangle?

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3

Does the pentomino contain a T-tetromino?

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4

: Does the pentomino have exactly 8 edges?

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F I L N P T U V W X Y Z

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
Jaap
Scherphuis
 

1

Does it have line symmetry?

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2


 

Does it fit inside this figure (a 3x3 square with a 1x2 corner missing)?
     x
     xxx
     xxx

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3
 

Count the number of squares with exactly two neighbouring squares, on opposing sides.
Is this an odd number?

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4
 

Count the number of squares with exactly two neighbouring squares, on non-opposing sides. Are there at least two such squares? 

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F I L N P T U V W X Y Z

1

N Y 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
Peter Sipos (Hongarije)

1

Does it have line symmetry?

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2

Is the adjacency graph of the constituting squares a path (node degrees < 3)?

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3

Is the area of the bounding rectangle less than 9?

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4

 

Can the following decamino be solved using this pentomino?
  

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F I L N P T U V W X Y Z

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 van de Wetering
Aad
v. d. Wetering

1

Do you have line symmetry?

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2

Do you fit inside a 3x3 square, touching all sides?

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3

Are the numbers of your squares' individual outer edges - sorted - 2-2-2-3-3?

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4



 

Do two copies fit inside a 2x5 rectangle and/or inside the figure shown below?
      X
      XXXX
      XXXX
             X

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F I L N P T U V W X Y Z

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

 


 


Berend Jan van der Zwaag

Berend Jan
 v. d. Zwaag
 

 

1

Does it contain two non-4-touching dominoes? (Touching at the corners is allowed.)

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2

Does it fit together with a heptomino in a 3x4 rectangle?

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3

Does it fit together with two copies of another pentomino in a 3x5 rectangle?

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4

Does it have line-symmetry?

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5

Can it be constructed using a domino and a straight tromino?

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6

Does it fit inside a 2x5 rectangle?

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7

Does it fit inside a 3x3 square?

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8

Does it fit together with a tromino and a tetromino in a 3x4 rectangle?

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9

Is its bounding rectangle a square?   

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10

Does it contain two non-8-touching dominoes? (Touching at the corners is not allowed.)

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11

Does it fit together with a domino and two monominoes in a 3x3 square?

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12

Does it fit twice in a 3x4 rectangle? 

Image

13

Does it fit together with a tromino and a domino in a 2x5 rectangle?

Image

14

Can two copies construct a decamino with a fully enclosed 1x1 hole?

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15

Can two copies construct a point-symmetric decamino with a fully enclosed 1x1 hole?

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F I L N P T U V W X Y Z

1

N Y Y Y N N Y Y Y N N Y

2

N N Y N Y Y Y Y N N Y N

3

N Y Y N N Y N Y N Y Y Y

4

N Y N N N Y Y Y Y Y N N

5

N Y Y Y Y Y N Y N N N N

6

N Y Y Y Y N Y N N N Y N

7

Y N N N Y Y Y Y Y Y N Y

8

N N Y N Y Y Y Y Y N Y N

9

Y N N N N Y N Y Y Y N Y

10

N Y Y N N N Y N N N N Y

11

Y N N N Y Y Y Y Y N N Y

12

N N Y Y Y N Y Y Y N Y N

13

N Y Y Y Y N N N N N Y N

14

Y N Y Y N Y Y N N N Y Y

15

Y N Y Y N Y N N N N Y Y

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.
 

Johan Viljoen
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


 

Martin Watson
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?

 


 

F I L N P T U V W X Y Z

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.

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