In the popular card game SET, there are 81 cards, each with a unique combination of 3 possible values for 4 attributes (number: 1,2,3; texture: solid, open, striped; color: red, green, purple, shape: rectangle, oval, squiggle). A valid set is three cards with, for each attribute, all 3 values the same, or all three different.
Simple combinatorics reveals that there are 1080 possible sets, and C(81,3)=83500 total groups of 3 cards. Thus if n=3 cards are dealt out,
1080 deals have 0 sets 84240 deals have 1 set
Exact enumerations are known for a few small values of n, but not for n=12, which the rules of SET specify as the starting deal. Randomized simulations show that about 3.2% of all 12-card SET deals have no sets. This project aims to figure out the exact number.
There are C(81,12)=70,724,320,184,700 (about 70 trillion) possible 12-card deals. In order to solve this problem within 24 hours will require a pace of over 800 million deals/second. Hopefully we can get within that order of magnitude using OpenCL to drive a GPU with a lot of cores.
For more information and inspiration go read The Joy of SET (Gordon&McMahon)!
To launch the jupyter notebook online, click here (may take a minute or two to create the virtual environment):
