# Circled

Author: daniyar
Problem has been solved: 13 times

Русский язык | English Language

Dima independently and uniformly at random picked 100 points $A_1, A_2, ..., A_{100}$ on some circle. After that, he connected segments $A_1A_2$, $A_2A_3$,....,$A_{100}A_1$ which divided circle into some regions. Let $n$ be the expected value of the number of regions bounded by straight lines. Find $[3n]$.