Triple Pentominoes
Livio Zucca

Pento-Tetro-Trominoes

We are searching for the 220 shapes that can be covered by three different pentominoes at least. We'll give precedence to the solutions on the finite plane with the smallest surface. If there aren't solutions on the plane, we'll accept solutions on cylindrical surface or on Moebius strip. Solutions on torus are not interesting because each pentomino cover a torus. If you have better solutions, please send me HERE with gif, jpg, bmp, FidoCad or ascii-art format.



Update! Col. George Sicherman has found this
improved solution for V5W5Y5.

Please visit his Triple Pentominoes Update page for further updates.




Update! Col. George Sicherman has found an incredible solution which makes 8 pentominos compatible.


F5I5L5F5I5P5F5I5N5F5I5T5F5I5U5
F5I5V5F5I5W5F5I5X5F5I5Y5F5I5Z5
F5L5P5F5L5N5F5L5T5F5L5U5F5L5V5
F5L5W5F5L5X5F5L5Y5F5L5Z5F5P5N5
F5P5T5F5P5U5F5P5V5F5P5W5F5P5X5
F5P5Y5F5P5Z5F5N5T5F5N5U5F5N5V5
F5N5W5F5N5X5F5N5Y5F5N5Z5F5T5U5
F5T5V5F5T5W5F5T5X5F5T5Y5F5T5Z5
F5U5V5F5U5W5F5U5X5F5U5Y5F5U5Z5
F5V5W5F5V5X5F5V5Y5F5V5Z5F5W5X5
F5W5Y5F5W5Z5F5X5Y5F5X5Z5F5Y5Z5
I5L5P5I5L5N5I5L5T5I5L5U5I5L5V5
I5L5W5I5L5X5I5L5Y5I5L5Z5I5P5N5
I5P5T5I5P5U5I5P5V5I5P5W5I5P5X5
I5P5Y5I5P5Z5I5N5T5I5N5U5I5N5V5
I5N5W5I5N5X5I5N5Y5I5N5Z5I5T5U5
I5T5V5I5T5W5I5T5X5I5T5Y5I5T5Z5
I5U5V5I5U5W5I5U5X5I5U5Y5I5U5Z5
I5V5W5I5V5X5I5V5Y5I5V5Z5I5W5X5
I5W5Y5I5W5Z5I5X5Y5I5X5Z5I5Y5Z5
L5P5N5L5P5T5L5P5U5L5P5V5L5P5W5
L5P5X5L5P5Y5L5P5Z5L5N5T5L5N5U5
L5N5V5L5N5W5L5N5X5L5N5Y5L5N5Z5
L5T5U5L5T5V5L5T5W5L5T5X5L5T5Y5
L5T5Z5L5U5V5L5U5W5L5U5X5L5U5Y5
L5U5Z5L5V5W5L5V5X5L5V5Y5L5V5Z5
L5W5X5L5W5Y5L5W5Z5L5X5Y5L5X5Z5
L5Y5Z5P5N5T5P5N5U5P5N5V5P5N5W5
P5N5X5P5N5Y5P5N5Z5P5T5U5P5T5V5
P5T5W5P5T5X5P5T5Y5P5T5Z5P5U5V5
P5U5W5P5U5X5P5U5Y5P5U5Z5P5V5W5
P5V5X5P5V5Y5P5V5Z5P5W5X5P5W5Y5
P5W5Z5P5X5Y5P5X5Z5P5Y5Z5N5T5U5
N5T5V5N5T5W5N5T5X5N5T5Y5N5T5Z5
N5U5V5N5U5W5N5U5X5N5U5Y5N5U5Z5
N5V5W5N5V5X5N5V5Y5N5V5Z5N5W5X5
N5W5Y5N5W5Z5N5X5Y5N5X5Z5N5Y5Z5
T5U5V5T5U5W5T5U5X5T5U5Y5T5U5Z5
T5V5W5T5V5X5T5V5Y5T5V5Z5T5W5X5
T5W5Y5T5W5Z5T5X5Y5T5X5Z5T5Y5Z5
U5V5W5U5V5X5U5V5Y5U5V5Z5U5W5X5
U5W5Y5U5W5Z5U5X5Y5U5X5Z5U5Y5Z5
V5W5X5V5W5Y5V5W5Z5V5X5Y5V5X5Z5
V5Y5Z5W5X5Y5W5X5Z5W5Y5Z5X5Y5Z5



Here below we are searching for the shape of minimal area that can be covered by the maximal number of different pentominoes.


PLANE


CYLINDER


TORUS




Notice:

1) I just find this solutions on our website:
http://home.planetinternet.be/~demeod/conmeerlingen.html
so it isn't really of me. The most I got from Patrick Hamlyn whose found this quadruples by Peter Essers program and others are from Aad van de Wetering. [Odette De Meulemeester]

2) I can't attribute the exact paternity of these solutions. The author name on each drawing is of who signals the solution in this game. [Livio Zucca]

3) I think that from 66 pentomino-pentomino solutions (if they are minimal) then can be derived some for the 220 pentomino-pentomino-pentomino (minimal also). [Jorge L. Mireles]


See also:
Pento-tro-dominoes
Pento-tetro-trominoes
Tetrominoes Challenge


LINK:
Visit the wonderful site of Jorge Luis Mireles
The new pages of Giovanni Resta



_________________

It isn't trivial!

First edition: Dic 31th, 2003 - Last revision: Jan 11th, 2004

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