Eight players competed at a recent chess tournament. Knowing that:
Each player played all the others, exactly once.
Winning earns you 1 point; drawing, ½ point; and losing, 0 points.
Everybody ended with a different number of points.
The one who ended 2nd earned as many points as the four bottom players put together.
What was the result of the game between the player who ended 3rd and the player who ended 7th?
(In reply to One solution
If everyone beat all the others below him, scores would be 7, 6, 5, 4, 3, 2, 1, and 0, and the conditions of the problem would still be true... so your solution cannot be the only one.
(OTOH, in this solution the 3rd also defeated the 7th, so that part may (must?) be right.)