Let n2 be an integer.

Question

Let $n>2$ be an integer. Suppose there are $n$ Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Each pair of nearest stations is connected by a blue line, while all remaining pairs are connected by a red line. If the number of red lines is 99 times the number of blue lines, then the value of $n$ is:

Accepted Answer

Blue lines (adjacent pairs): $n$.

Red lines (all other pairs): $\binom{n}{2}-n$.

$$\binom{n}{2}-n = 99n \implies \frac{n(n-1)}{2} = 100n \implies n-1=200 \implies n=201$$

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