EvenQuads is a SET-like card game published by the AWM whose goal is to find “quads”, which are sets of four cards satisfying a particular pattern. The cards can be viewed as points in the finite affine geometry AG(6,2), and a quad in the card game corresponds to a plane in AG(6,2). We are most interested in quad-free collections of cards, which turn out to be Sidon Sets. We will describe an analog of the “Cap Set problem” for EvenQuads, and discuss known results. In particular, we will address the question of how many cards you must lay down to guarantee a quad.

This is based on joint work with Kariane Calta, Julia Crager, Felicia Flores, Lauren L. Rose, Daniel Rose-Levine, Darrion Thornburgh, and Raphael Walker.