Saturday, March 21, 2009

March Math Madness

How many games in the NCAA tourney? Assuming we don’t count the play-in game for the 64th spot you can count up 32+ 16+ 8 + 4 + 2 + 1 and get 63.

It’s easy to determine the number of games played to determine a champion in a single elimination tournament. Say there are 64 teams in the tournament. When a team loses they are out so 63 teams must lose to determine the champ. That means 63 games are needed.

In general, if there are N teams in a single elimination tournament, you need to play N-1 games to get a champ.

If you want to make sure you have a perfect bracket you’d need to do every possible combination. With the play-in game, there are 64 games played. There are two possible outcomes for each game so the possible outcomes are 2 to the 64th power or about 18 quintillion.