MathDB
CHMMC 2022 Winter / 2022-23 Team #1

Source:

August 10, 2023
algebra

Problem Statement

A wall contains three switches A,B,CA,B,C, each of which powers a light when flipped on. Every 2020 seconds, switch AA is turned on and then immediately turned off again. The same occurs for switch BB every 2121 seconds and switch CC every 2222 seconds. At time t=0t = 0, all three switches are simultaneously on. Let t=T>0t = T > 0 be the earliest time that all three switches are once again simultaneously on. Compute the number of times t>0t > 0 before TT when at least two switches are simultaneously on.