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# In a basketball tournament, each of 4 players must play each

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In a basketball tournament, each of 4 players must play each [#permalink]  23 Feb 2006, 03:21
In a basketball tournament, each of 4 players must play each of the other players exactly once. If no game ended in a tie, did someone win one and lose two games?

I. No one won all the games
II. No one lost all games
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Interesting one. I found B.

Number of games is: 4C2=6

Let's consider that a player has 1 point if he wins and 0 if he loses.
Pi is the score of player i.
We have: P1+P2+P3+P4=6 with 0<=Pi<=3
Pi wins one and loses two if Pi=1

1) Pi<3
We can have the situation where: P1=P2=P3=2 and P4=0
or P1=P2=2 and P4=P3=1
Insufficient.

2) Pi>0
We can't have Pi=>2 or else P1+P2+P3+P4=>8
There must be Pi=1
Sufficient.
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