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Cono Sur Olympiad
2003 Cono Sur Olympiad
5
5
Part of
2003 Cono Sur Olympiad
Problems
(1)
Coloring a triangular arrangement of circles
Source: Cono Sur 2003 #5
11/18/2015
Let
n
=
3
k
+
1
n=3k+1
n
=
3
k
+
1
, where
k
k
k
is a positive integer. A triangular arrangement of side
n
n
n
is formed using circles with the same radius, as is shown in the figure for
n
=
7
n=7
n
=
7
. Determine, for each
k
k
k
, the largest number of circles that can be colored red in such a way that there are no two mutually tangent circles that are both colored red.
combinatorics
cono sur