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Dutch Mathematical Olympiad
2001 Dutch Mathematical Olympiad
1
1
Part of
2001 Dutch Mathematical Olympiad
Problems
(1)
tournament 3-1-0 points, total 15 points, last 1 point, 2nd to las undefeated
Source: Dutch NMO 2001 p1
9/21/2019
In a tournament, every team plays exactly once against every other team. One won match earns
3
3
3
points for the winner and
0
0
0
for the loser. With a draw both teams receive
1
1
1
point each. At the end of the tournament it appears that all teams together have achieved
15
15
15
points. The last team on the final list scored exactly
1
1
1
point. The second to last team has not lost a match. a) How many teams participated in the tournament? b) How many points did the team score in second place in the final ranking?
combinatorics
algebra