ASU 066 All Russian MO 1965 tourist in Moscow
Source:
June 19, 2019
combinatorics
Problem Statement
The tourist has come to the Moscow by train. All-day-long he wandered randomly through the streets. Than he had a supper in the cafe on the square and decided to return to the station only through the streets that he has passed an odd number of times. Prove that he is always able to do that.