12 Pentominoes Tile an 8x8 Square with Hole
a MATLAB program which
sets up a problem in which an 8x8 square with 2x2 central hole
is to be tiled by the 12 distinct pentominoes.
Because this problem results in a large linear system to be solved,
we simply set up the linear system, write it to an LP file, and have
CPLEX compute solutions. The resulting solutions are then read by
CPLEX_SOLUTION_READ, and can be printed or plotted.
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
polyomino_multihderal_example_pentomino is available in
a MATLAB version.
Related Data and Programs:
is given the one-letter code for a pentomino, and returns a
corresponding shape matrix.
cleans up a matrix that represents a polyomino by setting all nonzero
entries to 1, and removing initial and final rows and columns of zeros.
for each possible embedding, lists the translation necessary to
to apply to the polyomino.
reports the number of ways a polyomino can be embedded in a region.
computes an index for each nonzero polyomino entry.
writes an LP file describing a particular problem.
computes the linear system for the pentomino example.
plots the solutions of the pentomino example.
prints the solutions of the pentomino example.
determines the matrix and right hand side for a polyomino multihedral
prints a tiling of a region R by a set of polyominoes P, based on a solution
computed by polyomino_multihedral.
carries out reflections and rotations of a set of polyominoes to
determine which transformations yield distinct variants.
prints a polyomino.
carries out reflections and rotations of a polyomino.
prints a set of polyominoes.
prints the current YMDHMS date as a timestamp.
Examples and Tests:
Last revised on 10 June 2018.