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Subset No Two Differ by 2

1800SpecialistCombinatoricsCounting Principles

AMC 10 A

Let $S$ be a subset of $\{1, 2, 3, \dots, 2024\}$ such that the following two conditions hold: * If $x$ and $y$ are distinct elements of $S$, then $|x - y| > 2$. * If $x$ and $y$ are distinct odd elements of $S$, then $|x - y| > 6$. What is the maximum possible number of elements in $S$? (A) 436 (B) 506 (C) 608 (D) 654 (E) 675
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