Triple Pentominoes
Livio Zucca
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.
improved solution for V5W5Y5.
Please visit his Triple Pentominoes Update page for further updates.
F5I5L5 | F5I5P5 | F5I5N5 | F5I5T5 | F5I5U5 |
F5I5V5 | F5I5W5 | F5I5X5 | F5I5Y5 | F5I5Z5 |
F5L5P5 | F5L5N5 | F5L5T5 | F5L5U5 | F5L5V5 |
F5L5W5 | F5L5X5 | F5L5Y5 | F5L5Z5 | F5P5N5 |
F5P5T5 | F5P5U5 | F5P5V5 | F5P5W5 | F5P5X5 |
F5P5Y5 | F5P5Z5 | F5N5T5 | F5N5U5 | F5N5V5 |
F5N5W5 | F5N5X5 | F5N5Y5 | F5N5Z5 | F5T5U5 |
F5T5V5 | F5T5W5 | F5T5X5 | F5T5Y5 | F5T5Z5 |
F5U5V5 | F5U5W5 | F5U5X5 | F5U5Y5 | F5U5Z5 |
F5V5W5 | F5V5X5 | F5V5Y5 | F5V5Z5 | F5W5X5 |
F5W5Y5 | F5W5Z5 | F5X5Y5 | F5X5Z5 | F5Y5Z5 |
I5L5P5 | I5L5N5 | I5L5T5 | I5L5U5 | I5L5V5 |
I5L5W5 | I5L5X5 | I5L5Y5 | I5L5Z5 | I5P5N5 |
I5P5T5 | I5P5U5 | I5P5V5 | I5P5W5 | I5P5X5 |
I5P5Y5 | I5P5Z5 | I5N5T5 | I5N5U5 | I5N5V5 |
I5N5W5 | I5N5X5 | I5N5Y5 | I5N5Z5 | I5T5U5 |
I5T5V5 | I5T5W5 | I5T5X5 | I5T5Y5 | I5T5Z5 |
I5U5V5 | I5U5W5 | I5U5X5 | I5U5Y5 | I5U5Z5 |
I5V5W5 | I5V5X5 | I5V5Y5 | I5V5Z5 | I5W5X5 |
I5W5Y5 | I5W5Z5 | I5X5Y5 | I5X5Z5 | I5Y5Z5 |
L5P5N5 | L5P5T5 | L5P5U5 | L5P5V5 | L5P5W5 |
L5P5X5 | L5P5Y5 | L5P5Z5 | L5N5T5 | L5N5U5 |
L5N5V5 | L5N5W5 | L5N5X5 | L5N5Y5 | L5N5Z5 |
L5T5U5 | L5T5V5 | L5T5W5 | L5T5X5 | L5T5Y5 |
L5T5Z5 | L5U5V5 | L5U5W5 | L5U5X5 | L5U5Y5 |
L5U5Z5 | L5V5W5 | L5V5X5 | L5V5Y5 | L5V5Z5 |
L5W5X5 | L5W5Y5 | L5W5Z5 | L5X5Y5 | L5X5Z5 |
L5Y5Z5 | P5N5T5 | P5N5U5 | P5N5V5 | P5N5W5 |
P5N5X5 | P5N5Y5 | P5N5Z5 | P5T5U5 | P5T5V5 |
P5T5W5 | P5T5X5 | P5T5Y5 | P5T5Z5 | P5U5V5 |
P5U5W5 | P5U5X5 | P5U5Y5 | P5U5Z5 | P5V5W5 |
P5V5X5 | P5V5Y5 | P5V5Z5 | P5W5X5 | P5W5Y5 |
P5W5Z5 | P5X5Y5 | P5X5Z5 | P5Y5Z5 | N5T5U5 |
N5T5V5 | N5T5W5 | N5T5X5 | N5T5Y5 | N5T5Z5 |
N5U5V5 | N5U5W5 | N5U5X5 | N5U5Y5 | N5U5Z5 |
N5V5W5 | N5V5X5 | N5V5Y5 | N5V5Z5 | N5W5X5 |
N5W5Y5 | N5W5Z5 | N5X5Y5 | N5X5Z5 | N5Y5Z5 |
T5U5V5 | T5U5W5 | T5U5X5 | T5U5Y5 | T5U5Z5 |
T5V5W5 | T5V5X5 | T5V5Y5 | T5V5Z5 | T5W5X5 |
T5W5Y5 | T5W5Z5 | T5X5Y5 | T5X5Z5 | T5Y5Z5 |
U5V5W5 | U5V5X5 | U5V5Y5 | U5V5Z5 | U5W5X5 |
U5W5Y5 | U5W5Z5 | U5X5Y5 | U5X5Z5 | U5Y5Z5 |
V5W5X5 | V5W5Y5 | V5W5Z5 | V5X5Y5 | V5X5Z5 |
V5Y5Z5 | W5X5Y5 | W5X5Z5 | W5Y5Z5 | X5Y5Z5 |
Here below we are searching for the shape of minimal area that can be covered by the maximal number of different pentominoes.
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