edit 2023/06/17: I elaborated a bit more in the conclusion about the open problem of finding a minimal κ \kappa .
I visited A Coruña last week for the Web Engines Hackfest and to participate to internal events with my fellow Igalians. One of our tradition being to play board games, my colleague Ioanna presented a card game called Set . To be honest I was not very good at it, but it made me think of a potential generalization for infinite sets that is worth a blog post…
Basically, we have a deck of λ μ \lambda^\mu cards with μ = 4 \mu = 4 features (number of shapes, shape, shading and color), each of them taking λ = 3 \lambda = 3 possible values (e.g. red, green or purple for the color). Given κ \kappa cards on the table, players must extract λ \lambda cards forming what is called a Set , which is defined as follows: for each of the μ \mu features, either the cards use the same value or they use pairwise distinct values.