An infinite number of sports fans with typewriters
From NY Times:
Mike Breen, a mathematician at the American Mathematical Society in Providence, R.I., said the chances of being one of the people who correctly picked the Final Four in ESPN.com's contest this year were about 1 in 750,000. Last year, he said, roughly 1 in 700 brackets included the correct four teams.
Note that there are 69,632 (= 16^3 * 17) possible combinations of Final Four teams. If you picked your Final Four bracket randomly, you would be ten times more likely to get it right than the folks participating in ESPN's contest.
Of course, last year the random strategy would have sucked.