ASU 290 All Soviet Union MO 1980 settlements on bank of Big Round Lake
Source:
July 19, 2019
combinatoricscombinatorial geometry
Problem Statement
There are several settlements on the bank of the Big Round Lake. Some of them are connected with the regular direct ship lines. Two settlements are connected if and only if two next (counterclockwise) to each ones are not connected. Prove that you can move from the arbitrary settlement to another arbitrary settlement, having used not more than three ships.