Problem of the Week 1131

Four-Way Tennis Match

Alice, Bob, Charlie, and Diane play tennis in sets. Two of them play a set, and the winner stays on the court for the next set, with the loser replaced by the player who was idle the longest.

At the end of the day, Alice played 61 sets, Bob played 22 sets, Charlie played 21 sets, and Diane played 20 sets. Who played in the 33rd set?

Note: The choice of the first two players is random, as is the choice of the two idle players to choose who plays in the second set.

Challenge: Find a harder variation still, but retaining the elegance of giving no information on the total number of sets won or the order play.

Source: Problem 33 in Dick Hess's nice book, All-Star Mathlete Puzzles, Sterling, 2009.

© Copyright 2010 Stan Wagon. Reproduced with permission.