SUMS: Gardiner -- Four-Dimensional Doughnut Tic-Tac-Toe

This week’s SUMS talk is being given by Sean Gardiner.  

Abstract: SET is a set-finding card game invented by geneticist Marsha Falco in 1974.
Each card displays a number of coloured, shaded shapes, and each of these four
attributes can take three different possible values.  A set is then any triple in which
for each attribute, either all three match, or all three differ.  

This talk will demonstrate how the game of SET is really just a four-dimensional version
of toroidal noughts and crosses in disguise, and will answer some of the natural
combinatorial questions that arise along the way.  Particular emphasis will be given to
the problem of determining how many cards must be drawn before a set is guaranteed
amongst them, which is analogous to determining maximal caps in n-dimensional finite
fields (which is an unsolved problem over F_3 for n>5).