1989 USAMO Problems/Problem 2
Problem
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
Solution
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.
See also
| 1989 USAMO (Problems • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
