MathDB

A table tennis tournament has

101

contestants, where each pair of contestants will play each other exactly once. In each match, the player who gets

11

points first is the winner, and the other the loser. At the end of the tournament, it turns out that there exist matches with scores

11

0

and

11

10

. Show that there exists 3 contestants

A,B,C

such that the score of the losers in the matches between

A,B

and

A,C

are equal, but different from the score of the loser in the match between

B,C

Problem Statement