Raymond Hall

Statement

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.

Artworks

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.