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2025 AMC 10A Problems/Problem 24: Difference between revisions

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Call a positive integer fair if no digit is used more than once, it has no <imath>0</imath>s, and no digit is adjacent to two greater digits. For example, <imath>196, 23</imath> and <imath>12463</imath> are fair, but <imath>1546, 320,</imath> and <imath>34321</imath> are not. How many fair positive integers are there?


<imath>\textbf{(A) } 511 \qquad \textbf{(B) } 2584 \qquad \textbf{(C) } 9841 \qquad \textbf{(D) } 17711 \qquad \textbf{(E) } 19682</imath>

Revision as of 12:18, 6 November 2025

Call a positive integer fair if no digit is used more than once, it has no $0$s, and no digit is adjacent to two greater digits. For example, $196, 23$ and $12463$ are fair, but $1546, 320,$ and $34321$ are not. How many fair positive integers are there?

$\textbf{(A) } 511 \qquad \textbf{(B) } 2584 \qquad \textbf{(C) } 9841 \qquad \textbf{(D) } 17711 \qquad \textbf{(E) } 19682$

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