00:01
On this problem, we are told that we have a tournament in which every player meets every other player exactly one time.
00:06
We want to know how many players can participate in a tournament of 45 matches.
00:11
Now, if we have x players, there's two players per match, and so that means the total number of matches would be x choose two.
00:26
That's just the total number of different ways of choosing two players for each match.
00:31
And since order doesn't matter, we use a combination other than a permutation.
00:36
Now we want this to be equal to 45, and so we want x choose 2 to be equal to 45.
00:45
And so x factorial over 2 factorial, x minus 2 factorial, is equal to 45.
00:56
Now x factorial over x minus 2 factorial leaves us with x times x minus 1, because x minus 2 on down will cancel.
01:06
And 2 factorial is 2.
01:07
So x times x minus 1 over 2 is equal to 45...
