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From: Doctor Paul Subject: Re: NCAA tournament possibilities? A great question at a wonderful time of the year! First notice that the 64 teams play 63 total games: 32 games in the first round, 16 in the second round, 8 in the 3rd round, 4 in the regional finals, 2 in the final four, and then the national championship game. 32+16+8+4+2+1= 63 Now let's answer an easier question. If there were four teams, and they played three games, how many different ways would there be to fill out a bracket? You can write them down. There are only eight of them. Where do that eight come from? Well, there are three games, and you have two possible choices for each game. Hence, 2^3 = 8 possibilities. Now back to the real tournament. Since there are 63 games to be played, and you have two choices at each stage in your bracket, there are 2^63 different ways to fill out the bracket. 2^63 = 9,223,372,036,854,775,808 That's more than nine quintillion possibilities. Perhaps now you can see why CNNSI is so willing to give away ten million dollars to the person that fills out a perfect bracket. It's just not likely to happen. Even if every person in America filled one out (300 million people), the probability of someone winning is: 300,000,000 ----------- = .00000000003253 2^63 I don't think anyone is going to fill out a perfect bracket any time soon. - Doctor Paul, The Math Forum http://mathforum.org/dr.math/