2009 ToT Spring Junior A P5 knights guard a 9-tower circular wall
Source:
March 7, 2020
combinatorics
Problem Statement
A castle is surrounded by a circular wall with towers which are guarded by knights during the night. Every hour the castle clock strikes and the guards shift to the neighboring towers, each guard always moves in the same direction (either clockwise or counterclockwise). Given that (i) during the night each knight guards every tower (ii) at some hour each tower was guarded by at least two knights (iii) at some hour exactly towers were guarded by single knights, prove that at some hour one of the towers was unguarded.