Each edge and each diagonal of the convex n-gon (n≥3) is colored in red or blue. Prove that the vertices of the n-gon can be labeled as A1,A2,...,An in such a way that one of the following two conditions is satisfied:
(a) all segments A_1A_2,A_2A_3,...,A_{n\minus{}1}A_n,A_nA_1 are of the same colour.
(b) there exists a number k,1<k<n such that the segments A_1A_2,A_2A_3,...,A_{k\minus{}1}A_k are blue, and the segments A_kA_{k\plus{}1},...,A_{n\minus{}1}A_n,A_nA_1 are red. combinatorics proposedcombinatorics