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 teams begin the tournament?

There are 6 rounds with two teams playing in the final round.
The number of teams in any round is twice that in the previous round. Therefore: Round 6 has 2 teams
Round 5 has 4 teams
Round 4 has 8 teams
Round 3 has 16 teams
Round 2 has 32 teams
Round 1 has 64 teams

Another way to look at it is there must be  teams that start the tournament.