Lesson 4

Problem. What is the maximum number of integers that can be marked among the numbers \(1,2,\dotsc,50\) so that none of the marked numbers equals twice another marked number? Try it! Using set theory notation, one may state this problem as follows: find \[\max\{|S| \colon S \subseteq \{1, \dotsc, 50\} \text{ and }\forall x,y \in S,\ x \neq 2y\} \ .\]