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Difference between revisions of "2024 AMC 10A Problems/Problem 20"

m (Protected "2024 AMC 10A Problems/Problem 20" ([Edit=Allow only administrators] (expires 04:59, 8 November 2024 (UTC)) [Move=Allow only administrators] (expires 04:59, 8 November 2024 (UTC))) [cascading])
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==Problem==
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Let <math>S</math> be a subset of <math>\{1, 2, 3, \dots, 2024\}</math> such that the following two conditions hold:
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- If <math>x</math> and <math>y</math> are distinct elements of <math>S</math>, then <math>|x-y| > 2</math>
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- If <math>x</math> and <math>y</math> are distinct odd elements of <math>S</math>, then <math>|x-y| > 6</math>.
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What is the maximum possible number of elements in <math>S</math>?
  
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<math>
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\textbf{(A) }436 \qquad
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\textbf{(B) }506 \qquad
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\textbf{(C) }608 \qquad
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\textbf{(D) }654 \qquad
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\textbf{(E) }675 \qquad</math>

Revision as of 16:06, 8 November 2024

Problem

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 $S$?

$\textbf{(A) }436 \qquad \textbf{(B) }506 \qquad \textbf{(C) }608 \qquad \textbf{(D) }654 \qquad \textbf{(E) }675 \qquad$

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