Higher-Dimensional Tic-Tac-Toe | Infinite Series

Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Regular tic-tac-toe can get a bit boring -- if both players are playing optimally, it always ends in a draw. But what happens if you increase the width of the board? Or increase the dimension of the board? Or increase both? Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episode How the Axiom of Choice Gives Sizeless Sets | Infinite Series https://www.youtube.com/watch?v=hcRZadc5KpI The standard game of tic-tac-toe is too easy. How can we, as mathematicians, play with the combinatorics of tic-tac-toe? There are (at least) three easy ways to modify the game of tic-tac-toe: increase the width of the board - like *this* 5x5 board - increase the dimension of the board - like *this* 3x3x3 board - or increase both, like this 4x4x4 board. Challenge Winner of the How the Axiom of Choice Gives Sizeless Sets: For Your Math Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com) Resources: Hales/Jewett paper: http://www.ams.org/journals/tran/1963-106-02/S0002-9947-1963-0143712-1/S0002-9947-1963-0143712-1.pdf Golomb/Hales paper: http://library.msri.org/books/Book42/files/golomb.pdf https://www.youtube.com/watch?v=p1YzYLzRwtk http://www.austms.org.au/Gazette/2005/Jul05/mathellaneous.pdf Special Thanks: Benjamin Houston-Edwards and Nathan Kaplan Mathologer Video: https://www.youtube.com/watch?v=aDOP0XynAzA Special thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level! And thanks to Mauricio Pacheco and Nicholas Rose who are supporting us on Patreon at the Lemma level!