In the final results of an eight-player chess tournament, there were no ties, and the second-place finisher scored as many points as the last four combined. What was the result of the match between the 3rd and 7th place finishers?
In the chess tournament, a total of eight participants took part, so the first-place finisher could have earned a maximum of 7 points. If he beat the second-place finisher, then the latter could have had a maximum of 6 points. If their match ended in a draw, the first could have earned a maximum of 6.5 points, and since there was no tie in the tournament, the second could have had a maximum of 6 points. Finally, if the second-place finisher defeated the first, then the first could have had a maximum of 6 points, and the second could have had a maximum of 5.5 points. Therefore, we can conclude that the second-place finisher scored a maximum of 6 points.

At the same time, we know that his score is equal to the total score of the last four finishers. They played 6 matches among themselves, so they scored at least 6 points in total. From these two results, it is clear that the second-place finisher scored 6 points, and the last four finishers scored this much in total. This, however, means that each of the top four finishers defeated the last four finishers, and thus the match between the 3rd and 7th place finishers was won by the former.

Based on the work of Zsolt Széles (Zalaegerszeg, Ady E. Secondary School, 8th grade)