2025 AMC 10A Problem 24

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

\textbf{(A)} 511 \qquad \textbf{(B)} 2{,}584 \qquad \textbf{(C)} 9{,}841 \qquad \textbf{(D)} 17{,}711 \qquad \textbf{(E)} 19{,}682

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.