Question 14
Let $n$ be a positive integer. Points $A_1, A_2, \dots, A_n$ are located on the inside of a circle, and points $B_1, B_2, \dots, B_n$ are on the circle, so that the segments $\overline{A_1B_1}$, $\overline{A_2B_2}$, \dots, $\overline{A_nB_n}$ are mutually disjoint. A grasshopper can jump from point $A_i$ to point $A_j$ (for $i, j \in \{1, \dots, n\}, i \neq j$) if and only if the segment $\overline{A_iA_j}$ does not go through any of the inner points of the segments $\overline{A_1B_1}, \overline{A_2B_2}, \dots, \overline{A_nB_n}$.
Show that the grasshopper can take a series of jumps to get from any point $A_i$ to any point $A_j$. (Russia 1994)
Show that the grasshopper can take a series of jumps to get from any point $A_i$ to any point $A_j$. (Russia 1994)