Pentomino Odd Triples

Livio Zucca's Pentomino Odd Pairs studies the problem of finding a compatibility figure for two pentominoes with an odd number of tiles. His Triple Pentominoes studies the problem of finding a compatibility figure for three pentominoes.

Here I combine Zucca's two problems and show compatibility figures for three pentominoes with an odd number of tiles!

The Master At Work

Zucca was the first to solve the case 5P+5X+5Y:

His solution has 61 tiles! Smaller solutions have since been found. See the table below.

Solutions

5F+5I+5L5F+5I+5N5F+5I+5P5F+5I+5T5F+5I+5U

13
5F+5I+5V5F+5I+5W5F+5I+5X5F+5I+5Y5F+5I+5Z

21
5F+5L+5N5F+5L+5P5F+5L+5T5F+5L+5U5F+5L+5V

11

7

19

11
5F+5L+5W5F+5L+5X5F+5L+5Y5F+5L+5Z5F+5N+5P

15

7

5
5F+5N+5T5F+5N+5U5F+5N+5V5F+5N+5W5F+5N+5X

25

27

15

9

33
5F+5N+5Y5F+5N+5Z5F+5P+5T5F+5P+5U5F+5P+5V

7

13

11

17

9
5F+5P+5W5F+5P+5X5F+5P+5Y5F+5P+5Z5F+5T+5U

7

19

7

13
5F+5T+5V5F+5T+5W5F+5T+5X5F+5T+5Y5F+5T+5Z

13
5F+5U+5V5F+5U+5W5F+5U+5X5F+5U+5Y5F+5U+5Z
5F+5V+5W5F+5V+5X5F+5V+5Y5F+5V+5Z5F+5W+5X
5F+5W+5Y5F+5W+5Z5F+5X+5Y5F+5X+5Z5F+5Y+5Z

13

17

21
5I+5L+5N5I+5L+5P5I+5L+5T5I+5L+5U5I+5L+5V

7
5I+5L+5W5I+5L+5X5I+5L+5Y5I+5L+5Z5I+5N+5P

11

11
5I+5N+5T5I+5N+5U5I+5N+5V5I+5N+5W5I+5N+5X
5I+5N+5Y5I+5N+5Z5I+5P+5T5I+5P+5U5I+5P+5V

13

29
5I+5P+5W5I+5P+5X5I+5P+5Y5I+5P+5Z5I+5T+5U

17

9
5I+5T+5V5I+5T+5W5I+5T+5X5I+5T+5Y5I+5T+5Z
5I+5U+5V5I+5U+5W5I+5U+5X5I+5U+5Y5I+5U+5Z
5I+5V+5W5I+5V+5X5I+5V+5Y5I+5V+5Z5I+5W+5X
5I+5W+5Y5I+5W+5Z5I+5X+5Y5I+5X+5Z5I+5Y+5Z
5L+5N+5P5L+5N+5T5L+5N+5U5L+5N+5V5L+5N+5W

5

13

11
5L+5N+5X5L+5N+5Y5L+5N+5Z5L+5P+5T5L+5P+5U

19

13

13
5L+5P+5V5L+5P+5W5L+5P+5X5L+5P+5Y5L+5P+5Z

7

7

7

23
5L+5T+5U5L+5T+5V5L+5T+5W5L+5T+5X5L+5T+5Y

15
5L+5T+5Z5L+5U+5V5L+5U+5W5L+5U+5X5L+5U+5Y
5L+5U+5Z5L+5V+5W5L+5V+5X5L+5V+5Y5L+5V+5Z

29
5L+5W+5X5L+5W+5Y5L+5W+5Z5L+5X+5Y5L+5X+5Z

13
5L+5Y+5Z5N+5P+5T5N+5P+5U5N+5P+5V5N+5P+5W

19

15

19

7
5N+5P+5X5N+5P+5Y5N+5P+5Z5N+5T+5U5N+5T+5V

33

7

21
5N+5T+5W5N+5T+5X5N+5T+5Y5N+5T+5Z5N+5U+5V
5N+5U+5W5N+5U+5X5N+5U+5Y5N+5U+5Z5N+5V+5W
5N+5V+5X5N+5V+5Y5N+5V+5Z5N+5W+5X5N+5W+5Y
5N+5W+5Z5N+5X+5Y5N+5X+5Z5N+5Y+5Z5P+5T+5U
5P+5T+5V5P+5T+5W5P+5T+5X5P+5T+5Y5P+5T+5Z

15

19
5P+5U+5V5P+5U+5W5P+5U+5X5P+5U+5Y5P+5U+5Z
5P+5V+5W5P+5V+5X5P+5V+5Y5P+5V+5Z5P+5W+5X

21
5P+5W+5Y5P+5W+5Z5P+5X+5Y5P+5X+5Z5P+5Y+5Z

11

15

29

11
5T+5U+5V5T+5U+5W5T+5U+5X5T+5U+5Y5T+5U+5Z
5T+5V+5W5T+5V+5X5T+5V+5Y5T+5V+5Z5T+5W+5X
5T+5W+5Y5T+5W+5Z5T+5X+5Y5T+5X+5Z5T+5Y+5Z
5U+5V+5W5U+5V+5X5U+5V+5Y5U+5V+5Z5U+5W+5X
5U+5W+5Y5U+5W+5Z5U+5X+5Y5U+5X+5Z5U+5Y+5Z
5V+5W+5X5V+5W+5Y5V+5W+5Z5V+5X+5Y5V+5X+5Z
5V+5Y+5Z5W+5X+5Y5W+5X+5Z5W+5Y+5Z5X+5Y+5Z

Last updated 2016-01-24.


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Col. George Sicherman [ HOME | MAIL ]