| course |
course_year |
question_number |
tags |
title |
year |
Markov Chains |
IB |
75 |
|
1.II.19H |
2008 |
The village green is ringed by a fence with $N$ fenceposts, labelled $0,1, \ldots, N-1$. The village idiot is given a pot of paint and a brush, and started at post 0 with instructions to paint all the posts. He paints post 0 , and then chooses one of the two nearest neighbours, 1 or $N-1$, with equal probability, moving to the chosen post and painting it. After painting a post, he chooses with equal probability one of the two nearest neighbours, moves there and paints it (regardless of whether it is already painted). Find the distribution of the last post unpainted.