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Five players $A$, $B$, $C$, $D$, $E$ participated in a chess tournament. It is known that all of the participants ended with a different amount of points, and that when ordered by them, they end up $ABCDE$. However, when ordered by the number of victories they obtained, they are placed in reverse order $EDCBA$.

For what $n$ could an analogous situation in a tournament with $n$ players happen?

My work so far:

$n=2$ – Impossible.

$n=3$ – Example:

Example for n = 3.

$n=5$ – Example:

Example for n = 5.

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  • I'm sorry, but the english of this post is near impossible to understand. – MT_ Aug 04 '16 at 17:20
  • If I understand correct, we have to construct a scenario that all players have a different number of points in a multiple-round-tournament. Moreover, the ranking by won games must be completely opposite to the ranking by points. – Peter Aug 04 '16 at 17:24
  • This would mean that the better a player was placed, the smaller (or at least not bigger) the number of won games is, which seems to be paradox at first sight. – Peter Aug 04 '16 at 17:25
  • @Peter: Yes, it is true – Roman83 Aug 04 '16 at 17:25
  • Maybe this exercise was made to show that candidate tournaments in this manner have major issues. – Peter Aug 04 '16 at 17:27
  • Please edit the problem so that it was clear – Roman83 Aug 04 '16 at 17:30

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