Problem 2: Suppose you are a member of an Olympic doubles badminton team. The setting we are considering is the 2012 Summer Olympics in London and your team is one of 16 teams competing. The teams are divided into 4 groups, A, B, C, and D, with four teams assigned to each group. Your team (YT) is in group A. In the preliminary round of competition, the four teams in each group compete in a round robin tournament (each team plays a match against the other 3 teams in their group). The two teams with the best records from cach group move to an elimination tournament. In the elimination tournament, the eight teams from the round robin tournament are matched for a quarterfinal. The four winners of the quarter-final matches advance to a semifinal. The two winners of the semifinal matches advance to a final match. The winner of the final match receives the gold medal; the loser receives the silver medal. The losing teams from the semifinal play each other to determine the bronze medal winner. Teams are matched in the elimination round as shown in the chart below, where "AI" and "A2" are the teams from group A with the best and second best record, respectively, in the group A round robin tournament. The other slots are determined the same way. Quarter Finals Semi-Finals Final 28 C2 B1 D2 A2 CI B2 D1 Suppose that your team (YT) is about to play the final round robin match of the tournament against another group A team (AA). Both teams are already guaranteed a slot in the quarter finals. The winner of this game will take the A1 slot and the loser will take the A2 slot. All other slots in the elimination round have been determined. However, there was a surprise upset in group D so that a highly ranked team has ended up in slot D2, and a low ranked team has taken the D1 slot.