SUMS (Sydney Uni Maths Society) talks are being held at 1pm each Thursday in New Law 104 this semester. Free pizza is on offer afterwards! This week’s talk is by Sean Gardiner. Abstract: SET is an award-winning 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 four-dimensional 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, surprisingly, is an unsolved problem over F_3 for n>5).