A theory of trios. – Math with Bad Drawings

Working on my book Math Games with Bad Drawings (by the way, for U.S. readers, two days left to preorder the deluxe package), I thought a lot about Set.

Maybe too much. I’ll let you judge.

Set is a classic pattern-hunting game. The cards have four traits: number, shape, color, and texture. Each trait comes in three flavors; for example, the shapes are squiggles, ovals, and diamonds, while the textures are filled, empty, and striped.

You lay out twelve cards, and then look for special trios called “sets,” where for every trait the three cards are either (a) all the same, or (b) all different.

For example, they might share three traits, and differ in one:

Or they might share two traits, and differ in the other two:

Or share a single trait, while differing in three:

Or differ in all four traits (the hardest kind of set to spot):

But watch out for deceptive not-quite-sets. If two cards share a trait while the third one differs, you’re out of luck.

The game was developed by geneticist Marsha Jean Falco in a moment of gorgeous serendipity. (I tell the story in the book.) Since then, it has become a favorite among mathematicians, who study its rich symmetries and peculiar generalizations to higher dimensions.

But personally, I’m most fascinated its potential as a Grand Unified Theory of Trios.

You see, pop culture is full of trios. Three friends will band together to fight noseless eugenicists.

Or to topple evil empires.

Or just to take on general crime and villainy.

To my eye, these trios resemble Sets. They share certain traits in common. On other traits, they all differ. But if two people share a special bond that the third does not… well, that’s poison for a friend group, isn’t it?

Maybe I’m shoehorning the world into my theory. Maybe fictional characters possess so many characteristics, and allow for so many interpretations, that you can always find a few shared and/or differing traits. Maybe this is all just an excuse to show off how amazingly good I have gotten at drawing scarves, lightsabers, and anthropomorphic chipmunks.

Or maybe Marsha Jean Falco gave the world something more than just a great card game: an organizing theory of friendship.

(Preorder the deluxe Math Games with Bad Drawings package through Kickstarter, or the still-thrilling ordinary version wherever you buy books!