Math Prize 2013 Problem 4
Source:
September 10, 2013
Problem Statement
The MathMatters competition consists of 10 players , , , competing in a ladder-style tournament. Player plays a game with : the loser is ranked 10th, while the winner plays . The loser of that game is ranked 9th, while the winner plays . They keep repeating this process until someone plays : the loser of that final game is ranked 2nd, while the winner is ranked 1st. How many different rankings of the players are possible?