OFFSET
1,4
COMMENTS
The problem of determining the maximum number of V-pentominoes (or the densest packing) covering the cells of the square n X n was proposed by A. Cibulis.
Problem for the squares 5 X 5, 6 X 6 and 8 X 8 was given in the Latvian Open Mathematics Olympiad 2000 for Forms 6, 8 and 5 respectively.
Solutions for the squares 3 X 3, 5 X 5, 8 X 8, 12 X 12, 16 X 16 are unique under rotation and reflection.
REFERENCES
A. Cibulis, Equal Pentominoes on the Chessboard, j. "In the World of Mathematics", Kyiv, Vol. 4., No. 3, pp. 80-85, 1998. (In Ukrainian), http://www.probability.univ.kiev.ua/WorldMath/mathw.html
A. Cibulis, Pentominoes, Part I, Riga, University of Latvia, 2001, 96 p. (In Latvian)
A. Cibulis, From Olympiad Problems to Unsolved Ones, The 12th International Conference "Teaching Mathematics: Retrospective and Perspectives", Šiauliai University, Abstracts, pp. 19-20, 2011.
EXAMPLE
There is no way to cover square 3 X 3 with more than just one V-pentomino so a(3)=1.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Juris Cernenoks, Jul 10 2012
STATUS
approved
