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 eac pentomino cover a torus. If you have better solutions, please write to George Sicherman HERE.

 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.

PLANE

CYLINDER

TORUS

Notice:

1) I just find this solutions on our website:
http://pentomino.classy.be/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:

_________________

It isn't trivial!

First edition: Dec. 31, 2003 — Last revision: Aug. 29, 2017

Hosted by Col. George Sicherman's Polyform Curiosities.