MathDB

A29 B30

Part of 2021 LMT Spring

Problems(1)

2021 Spring LMT Division A Problem 29, B Problem 30

Source:

1/22/2022
In a group of 66 people playing the card game Tractor, all 5454 cards from 33 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 XX. Find the largest integer nn such that the nnth root of XX is rational.
Proposed by Sammy Charney
Due to the problem having infinitely many solutions, all teams who inputted answers received points.
combinatorics