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Determine the probablity

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September 5, 2010
probabilitycombinatorics unsolvedcombinatorics

Problem Statement

A game consists in pushing a flat stone along a sequence of squares S0,S1,S2,...S_0, S_1, S_2, . . . that are arranged in linear order. The stone is initially placed on square S0S_0. When the stone stops on a square SkS_k it is pushed again in the same direction and so on until it reaches S1987S_{1987} or goes beyond it; then the game stops. Each time the stone is pushed, the probability that it will advance exactly nn squares is 12n\frac{1}{2^n}. Determine the probability that the stone will stop exactly on square S1987.S_{1987}.
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