MathGrit
ProblemsTechniquesPricing
Sign inGet started
Back to problems

Count monotonous positive integers

1425ApprenticeCombinatoricsCounting Principles

AMC 12B · 2017 · Problem 11

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?

Answer choices

A
1024
B
1524
C
1533
D
1536
E
2048
0 students attempted0% solvedRating 1425

Related practice paths

AMC 12 PracticeAdvanced high school contest practice and review.AMC 10 vs AMC 12Choose the right practice path and difficulty level.AIME Practice StrategyHow to improve accuracy on high-difficulty problems.

Ready to check your answer?

Create an account to submit answers, save history, and track your rating.

Progressive Hints5

Unlock hints one at a time — each reveals a little more without spoiling the solution.

Step-by-Step Solutions13

Multiple solution approaches with detailed walkthroughs, unlocked after you solve the problem.

AI-Powered Grading

Instant feedback on your answer — handles fractions, decimals, and equivalent forms.

Curated problem bank

Supported tracks for AMC, AIME, MATHCOUNTS, and olympiad-style training, plus global problem sources like UKMT, Euclid, and Kangaroo.