1. ## Tournament Rules

In a certain tournament a player mist be defeated three times to be eliminated. If 512 contestants enter the tournament what is the greatest number of games that could be played?

2. Say you only have 3 players.
The maximum number is: 2+2+2+1+1

If 4 then: 2+2+2+2+1+1+1

If 5 then: 2+2+2+2+2+1+1+1+1

We see that general formula is, if n>=3 players then:
(2+2+...+2)+(1+1+...1)

Where 2 appears n times and 1 appears n-1 times.
Thus,
2n+1(n-1) = 3n - 1

Thus, if you have 512 that means,
3(512)-1

3. Originally Posted by Spartan 68868
In a certain tournament a player mist be defeated three times to be eliminated. If 512 contestants enter the tournament what is the greatest number of games that could be played?
Assume that in a game one player wins and the other loses, that is no draws.

At the end of the tournament 511 players have each lost 3 games, and the
winner may have lost 0, 1 or 2 games. As each, and every game had a loser
then there were 3*511, 3*511+1 or 3*511+2 games, the largest of these is
3*511+2=3*512-1.

RonL