Here I want to recopilate all minimum (non trivial) solutions for the restricted problem by Junk Kato and Patrick Hamlyn
PROBLEM: We want to find the minimum quantity of replicas for each polyomino that we can put in a way that no piece or group of pieces can move
TRIVIAL SOLUTIONS:
If we can reduce an N-omino in a smallest N-omino and the pices are in same position, then we have a trivial solution, that we will not mention
BIBLIOGRAPHY:
1979, David Wells,, Recreations in Logic, Dover, New York
1991, David Wells, The Penguin Dictionary of Curious and Interesting Geometry, page 117, Interlocking Polyominoes
1994,October. Frits G"obel, Bernhard Wiezorke; Problems for Einstein, CFF 34, 8-9
1994, December, Annecke Treep; Anti-slide... a winner!, CFF 35, 28 and title-page
1995 December Los Acertijeros 74 of Rodolfo Kurchan
199? Mails to Nobnet, Rodolfo Kurchan, Junk Kato.
1999 Mail to Nobnet, May 7, Pentomino anti-slide by Jacques Haubrich
2001, October Erich Fiedman: Problem of the Month ( http://www2.stetson.edu/~efriedma/mathmagic/1001.html
PENTOMINO:
http://pentomino.wirisonline.net/indexe.html
TORSTEN SILLKE: The domino anti-slide problem
http://www.mathematik.uni-bielefeld.de/~sillke/PENTA/antislide-domino
ERICH FRIEDMAN PACKING CENTER
http://www2.stetson.edu/~efriedma/rigidrect/
2009 August/September,Junk Kato, personal communication.