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 re: What am I missing? (spoilers)
It is not stated that the player who finished first won all their games, but there is nothing in Bob's scenario that is inconsistent with the problem statement. So either there are multiple solutions, or this is one of the valid scenarios for producing the unique answer.
In fact, variations of Bob's scenario do not affect what must have been the outcome of the game between the 3rd and 7th place finishers. The last four finishers could, as a group, only gain points from any difference from Bob's scenario, but that would require that the 2nd place finisher gain points also, to match. The only person the 2nd place finisher could gain points from would be the 1st place finisher, but the only way that could happen would be if they tied in their game, which would have resulted in a tie with the first place finisher--not allowed by the puzzle statement.
So it looks like indeed the 2nd place finisher won his/her game against the 7th place finisher regardless of the scenario. And if it depended on the scenario (valid scenario consistent with the problem statement) then the puzzle answer would not have been well defined.
Edited on November 16, 2005, 2:59 pm
Posted by Charlie
on 2005-11-16 14:57:54