Chess Tournament

[BMAD]

Eight men had participated in the chess tournament. (Each meets each; draws are allowed, giving 1/2 of a point; winner gets 1.) Everyone has a different number of points. The second one has as many points as the four weakest participants together. 

 

What was the result of the play between the third prizer and the chess-player that have occupied the seventh place?

 

 

[DejMar]

With the givens, the result of the round robin chess match was the following:

1st 2nd 3rd 4th 5th 6th 7th 8th
 7   6   5   4   3   2   1   0
As the round robin consisted of 28 matches, the total number of points equals 28. As each player played in no more than 7 games, 7 is the maximum number of points a single player could score. Given that no player had the same number of points as another at the end of the tournament, and given that the player who ended in 2nd place with a number of points that equaled in total to that of the 5th, 6th, 7th and 8th place finishers, no other possibility could result.
The player winning 3rd place won 5 games, having lost to the 1st and 2nd place players, thus he must have won the game against the 7th place player.