MathDB

11.8

Part of 1994 All-Russian Olympiad Regional Round

Problems(1)

bug traveling in the circle

Source: Russia 1994

10/7/2008
Points A1,A2,...,An A_1,A_2, ... ,A_n inside a circle and points B1,B2,...,Bn B_1,B_2,...,B_n on its boundary are positioned so that the segments A1B1,A2B2,...,AnBn A_1B_1,A_2B_2, ... ,A_nB_n do not intersect. A bug can go from point Ai A_i to Aj A_j if the segment AiAj A_iA_j does not intersect any segment AkBk A_kB_k, k≠i,j k \neq i, j. Prove that the bug can go from any point Ap A_p to any point Aq A_q in a finite number of steps.
combinatorics unsolvedcombinatorics