If I decided that I wanted to fill out the perfect number of brackets to get every game correctly and i wanted to remove a few options from play (16 beating 1) how many brackets do I have to do. and how do I know? please show work.
In any single elimination tournament, the math works like this: First, determine how many games will be played. That is equal to the number of competitors minus one. The logic is simple, you eliminate one competitor per game played. You'll have one emerge unbeaten, and everyone else will lose once. So, 64 game field takes 63 games to determine a champion. If you had, say, 27 competitors, you'd need to play 26 games to determine the champion. The number of possible outcomes is 2 raised to the power of however many games are played. If you're playing 63 games, it's 2^63. Your calculator probably can't handle that, but type 2^63 into the google search box, and you'll get back 9.22337204 × 10^18, or (deep breath) 92,233,720,400,000,000,000 possible outcomes. And you wonder why there are never any perfect brackets. If you want to remove a few games from consideration, then just adjust the number of games in the equation accordingly. For example, if you just want to assume that 1 will beat 16 in all four of their matchups, then you'd calculate 2^59 instead of 2^63.
