3n participants in the Mathematical Olympiad competition
Source: Polish MO Recond Round 1984 p4
September 9, 2024
combinatorics
Problem Statement
There are participants in the Mathematical Olympiad competition. They are assigned seats in three rows, with seats in each, and are admitted into the hall one at a time, after which they immediately take their seats. Calculate the probability that until the last competitor takes his seat, at any moment for each two rows the difference in the number of players sitting in them is no greater than 1.