Difference between revisions of "2005 IMO Problems/Problem 6"
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In a mathematical competition, in which 6 problems were posed to the participants, every two of these problems were solved by more than 2/5 of the contestants. Moreover, no contestant solved all the 6 problems. Show that there are at least 2 contestants who solved exactly 5 problems each. | In a mathematical competition, in which 6 problems were posed to the participants, every two of these problems were solved by more than 2/5 of the contestants. Moreover, no contestant solved all the 6 problems. Show that there are at least 2 contestants who solved exactly 5 problems each. | ||
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| + | ==Solution== | ||
| + | {{solution}} | ||
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| + | ==YouTube== | ||
| + | https://youtu.be/gHfJYsxUM5o | ||
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| + | ==See Also== | ||
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| + | {{IMO box|year=2005|num-b=5|after=Last Problem}} | ||
Latest revision as of 22:25, 26 August 2024
Contents
Problem
In a mathematical competition, in which 6 problems were posed to the participants, every two of these problems were solved by more than 2/5 of the contestants. Moreover, no contestant solved all the 6 problems. Show that there are at least 2 contestants who solved exactly 5 problems each.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
YouTube
See Also
| 2005 IMO (Problems) • Resources | ||
| Preceded by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Last Problem |
| All IMO Problems and Solutions | ||
