CONO-SUR 2003 Problem 5

Let $n=3k+1$ , where $k$ is a positive integer. A triangular arrangement of side $n$ is formed using circles with the same radius, as is shown in the figure for $n=7$ . Determine, for each $k$ , 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.

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