1995 USAMO Problems/Problem 5
Problem
Suppose that in a certain society, each pair of persons can be classified as either amicable or hostile. We shall say that each member of an amicable pair is a friend of the other, and each member of a hostile pair is a foe of the other. Suppose that the society has 
persons and 
amicable pairs, and that for every set of three persons, at least one pair is hostile. Prove that there is at least one member of the society whose foes include 
or fewer amicable pairs.
Solution
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See Also
| 1995 USAMO (Problems • Resources) | ||
| Preceded by Problem 4 |
Followed by Last Problem | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
