Tetrominoes Challenge
Livio Zucca

Update!

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 send me HERE with gif, jpg, bmp, FidoCad or ascii-art format.

 ILNQ ILNT ILQT INQT LNQT ILN ILQ ILT INQ INT IQT LNQ LNT LQT NQT IL IN IQ IT LN LQ LT NQ NT QT

Notice:
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.