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My Disabilities

Everyone has their own struggles in life. My main roadblocks have been my four mental/neurological disorders. I have Tourette Syndrome, Obsessive-Compulsive Disorder, Bipolar Disorder, and Asperger Syndrome. While I have had very difficult times in my life, and have been hospitalized many times, I realize that my disabilities have helped shape the person I am today, and that while it may be tougher, I can accomplish anything in life that a "normal" person can. I choose to observe the many positives in my life, rather than the negatives: A loving and supportive family, an education, caring friends, and a place to call home. Many of my friends do not have all of these gifts. I will therefore continue to make progress in acheiving my goals, regardless of the difficulties I may experience along the way.

Welcome!

My name is David Smith, and here you can find information about me, my interests, and most importantly, my mathematical discoveries.

I am 21 years old, soon to be a college student majoring in mathematics and physics. My interests include mathematics, physics, computer programming, chess, retrograde analysis (a very logical and unique genre of chess problems), mechanical puzzles and computer puzzle games, speedcubing (the art of solving a Rubik's Cube as fast as possible), and blindfold cubing (the art of solving a Rubik's Cube blindfolded as fast as possible).

I plan to put all of my current and future mathematical discoveries on this website, as a way to organize my work and share it with others. So far, all of my results are about the combinatorics of higher-dimensional permutation puzzles, as this is a special interest of mine. I plan to continue in this area for some time, until I am more competent at doing proofs in higher-level mathematics.

My first discovery was to re-derive the three formulae already discovered by Chris Hardwick here. They count the number of reachable positions of an n x n x n Rubik's Cube, supercube, and super-supercube (See the link for an explanation of these terms). I am planning to put my explanation of how I derived these formulae here soon.

My second discovery was to find an upper bound for the number of reachable positions of the program Magic120Cell, created by my friend Roice Nelson. Roice has very kindly allowed me to store my papers on his website, which is very much appreciated. My explanation can be seen here in pdf format. (Requires Adobe Reader, a free download.)

I have just finished counting the number of ways the faces of a 120-cell can be colored using exactly or at most k colors and the number of functionally different Magic120Cell programs with exactly or at most k colors. My result is here; I am planning to write a more comprehensive paper that explains how I derived these formulae. My next project is to discover a formula for the number of reachable positions of each Magic120Cell program in which there are n pieces per edge (n must neccesarily be odd). After that, I plan to deduce the exact number of reachable positions of an n x n x n x n Rubik's Cube, supercube, and super-supercube; and then an upper bound for the number of reachable positions of an n^k Rubik's Cube, supercube, and super-supercube.

Thanks for visiting my website; I hope you found it interesting. I will keep updating it as I continue my work. If you have any comments, questions, or suggestions, feel free to email me at djs314djs314@gmail.com.