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National and Regional Contests
Turkey Contests
Turkey MO (2nd round)
2017 Turkey MO (2nd round)
1
1
Part of
2017 Turkey MO (2nd round)
Problems
(1)
Turkey NMO 2017 p1
Source:
1/26/2018
A wedding is going to be held in a city with
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types of meals, to which some of the
2017
2017
2017
citizens will be invited. All of the citizens like some meals and each meal is liked by at least one person. A "
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" is a set of citizens, such that each meal is liked by at least one person in the set. A "
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" is a set that contains at least one person from each "
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list
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". Given a "
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", which has no subset (other than itself) that is also a "
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", prove that there exists a meal, which is liked by everyone in the group.
combinatorics