2012 ToT Spring Junior A p3, guard on duty for n days in a row
Source:
March 4, 2020
combinatorics
Problem Statement
In a team of guards, each is assigned a different positive integer. For any two guards, the ratio of the two numbers assigned to them is at least . A guard assigned the number is on duty for days in a row, off duty for days in a row, back on duty for days in a row, and so on. The guards need not start their duties on the same day. Is it possible that on any day, at least one in such a team of guards is on duty?