2017 AMC 10B Problems/Problem 17

Problem

Call a positive integer 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?

$\textbf{(A)}\ 1024\qquad\textbf{(B)}\ 1524\qquad\textbf{(C)}\ 1533\qquad\textbf{(D)}\ 1536\qquad\textbf{(E)}\ 2048$

Solution

It adds in $9$ at the end, but we know since it is MAA, it is probably a troll question, so we look at the answers. $(C)$ looks likely, as it is just $(B)+9$ , but we remember that MAA is trolly so it is probably $\boxed{\textbf{(B) }1524}$ .

2017 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 16	Followed by Problem 18
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All AMC 10 Problems and Solutions

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2017 AMC 10B Problems/Problem 17

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