MathDB
Accounting for an overcount

Source: 2017 AMC 10B #17, AMC 12B #11

February 16, 2017
2017 AMC 10BAMC 10AMCcountingAMC 12AMC 12 B

Problem Statement

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?
<spanclass=latexbold>(A)</span> 1024<spanclass=latexbold>(B)</span> 1524<spanclass=latexbold>(C)</span> 1533<spanclass=latexbold>(D)</span> 1536<spanclass=latexbold>(E)</span> 2048<span class='latex-bold'>(A)</span> \text{ 1024} \qquad <span class='latex-bold'>(B)</span> \text{ 1524} \qquad <span class='latex-bold'>(C)</span> \text{ 1533} \qquad <span class='latex-bold'>(D)</span> \text{ 1536} \qquad <span class='latex-bold'>(E)</span> \text{ 2048}