My favorite math puzzles are those that seem impossible at first, but then can be solved using only a few simple deductions. This is one of those problems and requires no formal math training, only curiosity and patience.
Alice, Bob, and Cole want to play a series of tennis matches against each other. The problem is, they only have one court, so only two can play at a time. To make it fair, they will randomly decide two players to play in the first match. The loser will leave the court and be replaced by the person who was sitting out. The winner will then play the previously absent person. They continue this method until they run out of time.
Alice plays in 12 games, Bob plays in 11 games, and Cole plays in 7 games. Who played in the 7th game?
The solution is below. Take your time to solve this one! If you peek early, you hurt no one but yourself. Once you look, the problem is gone forever.
First, let’s figure out how many games there were in total. If I add each player’s games, then divide by 2, I get 15 matches of tennis. Since Cole only played 7 games (I’m not very good…), this means that 8 of the matches were between Alice and Bob. But also notice that a…
