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?

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- May 31st 2007, 01:53 PMSpartan 68868Tournament 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?

- May 31st 2007, 05:13 PMThePerfectHacker
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 - June 1st 2007, 01:34 AMCaptainBlack
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