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ISI Entrance Examination
2021 ISI Entrance Examination
1
1
Part of
2021 ISI Entrance Examination
Problems
(1)
A Tale of Three Cities
Source: ISI 2021 P1
7/18/2021
There are three cities each of which has exactly the same number of citizens, say
n
n
n
. Every citizen in each city has exactly a total of
(
n
+
1
)
(n+1)
(
n
+
1
)
friends in the other two cities. Show that there exist three people, one from each city, such that they are friends. We assume that friendship is mutual (that is, a symmetric relation).
combinatorics
isi