2024 SSMO Accuracy Round Problems/Problem 9
Problem
In the game of 
- set, there are 
unique cards, each card containing a 12 traits of variants 
and 
A full house in the game of Sset is defined to be a hand of cards in which for each trait, all cards in the hand either share the same variant or have all different variants. The number of hands that can be considered a full house in the game of set can be expressed as 
where 
and 
are positive integers and 
is minimized. Find 
