The Game of Set and some variations Numberphile

The article was written by a well-known author.

A well-known author wrote the article. the ones with the same color but different shapes

Today I want to show you these funky laser cut wooden tiles. You can see they all have different patterns and different squiggles, cut out in different sizes. I’m hopefully going to teach you a fun game that you can play with them. Before we get to the tile part, you may or may not know this game– it’s called Set. This is a card game beloved by mathematicians everywhere in the world. It was actually invented in 1974 by Marshall Falco, who was a geneticist and not a mathematician. She invented it while studying epilepsy and German Shepherds, which is very cool.

I want to take just a moment to explain the rules. If we look at the deck here, these cards are not like normal playing cards. If we wanted to describe them, we might notice that there are four characteristics that we need to describe. Each card has a color, a number of objects on it, an object with a certain shape, and an object with a certain shading.

The options for color are purple, green, or red. For the number of objects, there are three options: one, two, or three. For the shape, there are three options: oval, squiggle, or diamond. For the shading, there are three options: empty, striped, or solid. This means that there are exactly one card for every combination.

So, for each card, you can only have one characteristic per quality, and there are 81 cards total. Now, let’s see if you can find a set here. We’re looking for a collection of three cards such that in each category, the cards are either all the same or all different. That means in each of the four categories, you either have one of each option where they all match, and it doesn’t have to be the same for each category.

I think different types of sets pop out to different types of people. I often find much faster sets where all three colors are different, for some reason it’s just easier for me to find those versus the ones with the same color but different shapes.