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1976 Swedish Mathematical Competition
1
1
Part of
1976 Swedish Mathematical Competition
Problems
(1)
in a tournament every team plays every other team just once
Source: 1976 Swedish Mathematical Competition p1
3/26/2021
In a tournament every team plays every other team just once. Each game is won by one of the teams (there are no draws). Each team loses at least once. Show that there must be three teams
A
A
A
,
B
B
B
,
C
C
C
such that
A
A
A
beat
B
B
B
,
B
B
B
beat
C
C
C
and
C
C
C
beat
A
A
A
.
combinatorics