IMO 1987 LL ICE36
A game consists in pushing a flat stone along a sequence of
IMO 1987 LL ICE36
Origin: ICE
Problem
A game consists in pushing a flat stone along a sequence of squares S0, S1, S2, . . . that are arranged in linear order. The stone is ini- tially placed on square S0. When the stone stops on a square Sk it is pushed again in the same direction and so on until it reaches S1987 or goes beyond it; then the game stops. Each time the stone is pushed, the probability that it will advance exactly n squares is 1/2n. Determine the probability that the stone will stop exactly on square S1987.