Problem

Source: 2015 Cuba 1.3

Tags: combinatorics



A tourist traveling on a bus from the VIAZUL company arrived at the station in the city of Cienfuegos and immediately set out to take a walking tour of the city. After visiting the Terry theater in this city, decided to return to the station but walking only for blocks traveled an odd number of times in his previous walk. Can he do this on his return regardless. of the initial route?