a library has one exit and one entrance and a blackboard at each
Source: 1974 Hungary - Kürschák Competition p1
October 15, 2022
combinatorics
Problem Statement
A library has one exit and one entrance and a blackboard at each. Only one person enters or leaves at a time. As he does so he records the number of people found/remaining in the library on the blackboard. Prove that at the end of the day exactly the same numbers will be found on the two blackboards (possibly in a different order).