1989 USAMO Problems/Problem 2
The 20 members of a local tennis club have scheduled exactly 14 two-person games among themselves, with each member playing in at least one game. Prove that within this schedule there must be a set of 6 games with 12 distinct players
If there are 14 games with two people each, there must be 28 indistinct players. Since there are just 20 members, at most 8 players could have played in more than one game. That leaves at least games with distinct players.
|1989 USAMO (Problems • Resources)|
|1 • 2 • 3 • 4 • 5|
|All USAMO Problems and Solutions|