We are searching for the 25 shapes that can be covered by some tetrominoes AND NOT by the others. We'll give precedence to the solutions on the plane with the smallest surface. If you have better solutions, please write to George Sicherman HERE.
You can see here below, at left, the first IT solution with N= 10. Afterwards, Mike Reid produced two improvements, one with N=8 and the other with N=6. After few hours, I received the solutions of Helmut Postl and Remmert Borst, with N=6 also.
The Mike's solutions are probably direct, on the contrary Helmut and Remmert derived their solutions from others.
For Helmut's solution we can write:
IT = ILT & INT
(I OR T) = (I OR L OR T) AND (I OR N OR T)
for Remmert's solution:
IT = ILQT & INT
(I OR T) = (I OR L OR Q OR T) AND (I OR N OR T)
Proof that solutions with an odd number of tetrominoes cannot exist.
The demonstration is of Paolo Licheri.
Visit the wonderful site of Jorge Luis Mireles (archived).
Zucca's Challenge Problem for Polyiamonds
Zucca's Challenge Problem for Tetrahexes
Zucca's Challenge Problem for Extrominoes
Zucca's Challenge Problem for Polypents
It isn't trivial!
First edition: Dec. 24, 2003 — Last revision: Jan. 10, 2013
Hosted by Col. George Sicherman's Polyform Curiosities.