Guessing a number based on divisibility
Source: CMO 2023 P1
March 11, 2023
combinatoricsCMOCMO 2023
Problem Statement
William is thinking of an integer between 1 and 50, inclusive. Victor can choose a positive integer and ask William: "does divide your number?", to which William must answer truthfully. Victor continues asking these questions until he determines William's number. What is the minimum number of questions that Victor needs to guarantee this?