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MathNet 2023-part-07 — 187 problems (EN–VI) Question 19

Math Olympiad Vault · MathNet 2023-part-07 — 187 problems (EN–VI)

Question 19

11 points are given on a circle. Petryk numbered them with the numbers $1, 2, \ldots, 11$. After that, pairs of points were connected by segments: $1$ and $2$, $2$ and $3$, $\ldots$, $10$ and $11$, $11$ and $1$. What is the largest possible number of intersection points of these segments? The given 11 points are not counted as intersection points.

Question illustration
**Figure 4**