Difference between revisions of "2021 AMC 10B Problems/Problem 16"

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Call a positive integer an uphill integer if every digit is strictly greater than the previous digit. For example, <math>1357, 89, and 5</math> are all uphill integers, but <math>32, 1240, and 466</math> are not. How many uphill integers are divisible by <math>15</math>?
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<math>\textbf{(A)} ~4 \qquad\textbf{(B)} ~5 \qquad\textbf{(C)} ~6 \qquad\textbf{(D)} ~7 \qquad\textbf{(E)} ~8</math>

Revision as of 17:01, 11 February 2021

Call a positive integer an uphill integer if every digit is strictly greater than the previous digit. For example, $1357, 89, and 5$ are all uphill integers, but $32, 1240, and 466$ are not. How many uphill integers are divisible by $15$?

$\textbf{(A)} ~4 \qquad\textbf{(B)} ~5 \qquad\textbf{(C)} ~6 \qquad\textbf{(D)} ~7 \qquad\textbf{(E)} ~8$

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