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.

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)

Holeless Variants
George Sicherman

ILT	IT	LQT	QT

See also:

• Pento-tro-dominoes
• Pento-tetro-trominoes

LINK:
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

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It isn't trivial!

First edition: Dec. 24, 2003 — Last revision: Jan. 10, 2013