Question 163
In a game of chess, the winner gets 1 point and the defeated gets 0 points. In the event of a draw, each player receives $\frac{1}{2}$ points.
Fourteen chess players, no two of whom were the same age, held a competition in which everyone played against everyone else. After the competition was completed, a ranking list was created. Of two players with the same number of points, the younger one gets a better ranking.
After the competition, Jan noticed that the top three finishers received a total of as many points as the total number of points of the last nine players. Jörg noted that the number of games that ended in a draw was a maximum. Determine the number of drawn games.
Fourteen chess players, no two of whom were the same age, held a competition in which everyone played against everyone else. After the competition was completed, a ranking list was created. Of two players with the same number of points, the younger one gets a better ranking.
After the competition, Jan noticed that the top three finishers received a total of as many points as the total number of points of the last nine players. Jörg noted that the number of games that ended in a draw was a maximum. Determine the number of drawn games.