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National and Regional Contests
Bosnia Herzegovina Contests
Bosnia Herzegovina Team Selection Test
2013 Bosnia Herzegovina Team Selection Test
3
3
Part of
2013 Bosnia Herzegovina Team Selection Test
Problems
(1)
n+1 people knowing each other
Source: Bosnia and Herzegovina TST 2013 problem3
5/20/2013
Prove that in the set consisting of
(
2
n
n
)
\binom{2n}{n}
(
n
2
n
)
people we can find a group of
n
+
1
n+1
n
+
1
people in which everyone knows everyone or noone knows noone.
inequalities
induction
combinatorics proposed
combinatorics