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2017 AMC 10B Problem 17

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2017 AMC 10B Problem 17AMC 10 Step by Step

Name: Date: September 13, 2026

Basic Counting · difficulty 3 of 5 · about 5 min · position P16-20

Call a positive integer $\textbf{monotonous}$ if it is a one-digit number or its digits, when read from left to right, form either a strictly increasing or a strictly decreasing sequence. For example, $3$ , $23578$ , and $987620$ are monotonous, but $88$ , $7434$ , and $23557$ are not. How many monotonous positive integers are there?

A)
$1024$
B)
$1524$
C)
$1533$
D)
$1536$
E)
$2048$

2017 AMC 10B Problem 17

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