\(\qquad\)In a mathematical competition, in which \(6\) problems were posed to the participants, every two of these problems were solved by more than \(\frac25\) of the contestants. Moreover, no contestant solved all the \(6\) problems. \(\\\qquad\)Show that there are at least \(2\) contestants who solved exactly \(5\) problems each.
| Attributes | Олімпіадна |
|---|---|
| Source | International Mathematical Olympiad |
| Year | 2005 |
| Number | 6 |
| Difficulty | 10.0 |
| Themes |