Difference between revisions of "2005 IMO Problems/Problem 6"

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==Problem==
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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==
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{{solution}}
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==YouTube==
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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

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

https://youtu.be/gHfJYsxUM5o

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