MathDB

In a group of

6

people playing the card game Tractor, all

54

cards from

3

decks are dealt evenly to all the players at random. Each deck is dealt individually. Let the probability that no one has at least two of the same card be

X

. Find the largest integer

n

such that the

n

th root of

X

is rational.
Proposed by Sammy Charney
Due to the problem having infinitely many solutions, all teams who inputted answers received points.

Problem Statement