1985 USAMO Problems/Problem 4
Problem
There are 
people at a party. Prove that there are two people such that, of the remaining 
people, there are at least 
of them, each of whom knows both or else knows neither of the two. Assume that "know" is a symmetrical relation; 
denotes the greatest integer less than or equal to 
.
Solution
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See Also
| 1985 USAMO (Problems • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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. 
