Question 20
Let $S$ be a subset of $\{1, 2, 3, \ldots, 2024\}$ such that the following two conditions hold:
• If $x$ and $y$ are distinct elements of $S,$ then $|x - y| \gt 2.$
• If $x$ and $y$ are distinct odd elements of $S,$ then $|x - y| \gt 6.$
What is the maximum possible number of elements in $S?$
• If $x$ and $y$ are distinct elements of $S,$ then $|x - y| \gt 2.$
• If $x$ and $y$ are distinct odd elements of $S,$ then $|x - y| \gt 6.$
What is the maximum possible number of elements in $S?$