Over spring break, with nothing to do aside from study and sleep, I started playing the card game SET.
If you’re not familiar with the game, SET consists of a deck of 81 cards, each with different combinations of three variations of various traits (shape, number, shading, and color). Twelve cards are randomly laid face up in the center playing area, and each player searches for three cards with either identical or completely different individual traits. In other words, two cards cannot share an identical trait (e.g. both red) without the 3rd card being red as well.
The game is fast paced and very challenging. For some, it becomes a matter of simply memorizing various set combinations. Other players methodically count out possible sets and look to see if a necessary 3rd card completes it.
As I was playing with my family, we discussed some questions that occurred as we played. For example, if the whole deck was laid out, how many cards could be laid down without forming a set?
After spending two days trying to figure out the problem myself unsuccessfully, I researched it. Apparently, there was a proof written based on the game!
If you’re not familiar with the game, SET consists of a deck of 81 cards, each with different combinations of three variations of various traits (shape, number, shading, and color). Twelve cards are randomly laid face up in the center playing area, and each player searches for three cards with either identical or completely different individual traits. In other words, two cards cannot share an identical trait (e.g. both red) without the 3rd card being red as well.
The game is fast paced and very challenging. For some, it becomes a matter of simply memorizing various set combinations. Other players methodically count out possible sets and look to see if a necessary 3rd card completes it.
As I was playing with my family, we discussed some questions that occurred as we played. For example, if the whole deck was laid out, how many cards could be laid down without forming a set?
After spending two days trying to figure out the problem myself unsuccessfully, I researched it. Apparently, there was a proof written based on the game!
What’s unique about this proof is that (at least to the mathematically minded), the process for determining the answer to this question is relatively straightforward. The solution has roots and implications in many other branches of math.
It must be a great career, playing and analyzing games for a living. My amateurish approach proved that the task is much more difficult than it seems… for some people, at least.
It must be a great career, playing and analyzing games for a living. My amateurish approach proved that the task is much more difficult than it seems… for some people, at least.