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Baltic Way
2015 Baltic Way
7
7
Part of
2015 Baltic Way
Problems
(1)
Combinatorics
Source: Baltic Way 2015
11/8/2015
There are
100
100
100
members in a ladies' club.Each lady has had tea (in private) with exactly
56
56
56
of her lady friends.The Board,consisting of the
50
50
50
most distinguished ladies,have all had tea with one another.Prove that the entire club may be split into two groups in such a way that,with in each group,any lady has had tea with any other.
combinatorics