- They all have the same number, or they all have different numbers
- They all have the same symbol, or they all have different symbols
- They all have the same shading, or they all have different shadings
- They all have the same color, or they all have different colors

Playing the game involves pattern recognition, but there is a lot of mathematics lurking in the background. For example, some people like to deal the last card facedown, as it's possible to figure out what it is using the other cards on the table. You can ask a lot of combinatorial questions: What's the probability of producing a set from three randomly drawn cards? What's the largest group of cards you can put together without creating a set? How many unique sets are there in a deck? What are the odds that there will be no set after 12 cards are dealt? You can model the game using four-dimensional vectors over the finite field with 3 elements. You can create other versions, like Projective Set, based on other mathematical models.

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One of my favorite games based off of set is Swish (amazon affiliate link here), which strengthens spatial-recognition skills.

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