Pickleball Round Robin

Test Your Cognitive Skills

Kyle, Anna, and Neil got together for a round-robin pickleball tournament, where, as usual, the winner stays on after each game to play the person who sat out that game. At the end of their pickleball afternoon, Anna is exhausted, having played the last seven straight games. Kyle, who is less winded, tallies up the games played:

1. Kyle played 8 games
2. Anna played 12 games
3. Neil played 14 games

Who won the fourth game against whom?

Hint: How many total games were played?

Answer

We have three players in a round-robin pickleball tournament, where:

1. Kyle played 8 games
2. Anna played 12 games
3. Neil played 14 games

First, find out the total games played. When you add up the total games played by Anna, Kyle and Neil respectively, you get:

8 + 12 + 14 = 34

However, a round-robin pickleball tournament is played with two participants in each match. So,

34/2 = 17

When you have three players in a round-robin pickleball tournament, you can infer that each player has played at least every other game. With 17 total games being played, each of the three players must have played at least eight games in the tournament. In the diagram below, you see that Kyle played eight games.

One observation from the table - if Kyle had won any of the 8 games he participated in, you would have seen two or more successive shaded regions. But, as seen from the table, Kyle must have lost in all the 8 games.

∴ Kyle lost in the fourth game as well.

Now, we need to find Kyle's opponent in the fourth games.

As evident from the question and the table, Anna and Neil played against each other in every game that Kyle couldn't participate in, i.e. the unshaded squares. From the question, you know that Anna played in the last seven games successively.

∴ Anna played in match numbers 1, 3, 5, 7, 9, 11, 12, 13, 14, 15, 16, & 17.

Then, Neil must have played the rest of the games against Kyle. That means it was Neil who defeated Kyle in the fourth game.