Let n be a positive integer and let vectors v1, v2, …, vn be given in the plain. A flea originally sitting in the origin moves according to the following rule: in the ith minute (for i=1,2,…,n) it will stay where it is with probability 1/2, moves with vector vi with probability 1/4, and moves with vector −vi with probability 1/4. Prove that after the nth minute there exists no point which is occupied by the flea with greater probability than the origin.Proposed by Péter Pál Pach, Budapest
combinatoricsprobabilitykomal