The National Collegiate Athletic Association (NCAA) men's Division I basketball tournament, played in the United States each March, involves the best college teams in the nation, playing an elimination-style tournament. Games are played in rounds; winning teams in each round continue, while losers are eliminated. There are the following rounds: first round, second round, regional semifinal,

regional final, national semifinal, and national final. Many teams pair up to play games in the first round. Only the winners go on to play games in the second round, and only two teams survive to play in the final round. The winner of the final round becomes the national champion. From this information,

How many games are played in the tournament?

Since two teams play in each game there will be half the number of games in each round as there are teams: Therefore: Round 6 has 1 game
Round 5 has 2 games
Round 4 has 4 games
Round 3 has 8 games
Round 2 has 16 games
Round 1 has 32 games

The total number of games can be found by adding the six terms:
1 + 2+4 + 8 +16+32— 63 games.

Another way to look at it is that all 64 teams that start the tournament loose exactly one game, except for the national champion. Thus, since each loss represents one game, there are 64 — 1 = 63 games.