Raymond Hall
Physics and mathematics describe the real magic of the universe: For
the past few years I have been generating original video content of
extraordinary and surprising phenomena and posting them on the social
media platform Instagram. Each short of up to 60 seconds is designed,
via the simplest means possible, to invite exploration of the true and
astonishing nature of the physical world and the beauty of
mathematical relationships. As of July 2021, more than 2 million
subscribers follow @physicsfun on Instagram, my online museum of
science, math, and curiosity. My submission came about as part of an
exploration of the solutions for tiling a rectangle with colored
pentominoes and the creation of 3 color-mapped physical puzzles.
There are 12 planar shapes formed by connecting 5 squares edge to
edge with no overlap, made famous by Golomb who in 1953 coined the
term pentomino. In 1960 Brian and Haselgrove found exactly 2339
possible arrangements that fill a 6x10 rectangle. Muñiz showed
when using 3 colors there exists only 48 solutions that balance (3
groups of 4 pentominoes) for which similar colored pieces don't
touch. I found these 48 independent solutions can produce a tiling
of an 8x6 rectangular configuration of 6x10 solutions, making a
rectangle 60 unit squares wide by 48 unit squares tall, where only
coloring allows recognition of the pentomino shapes. A simple
backtracking algorithm found the following solution after checking
103 million configurations.