Monotone Numbers

Problem

Call a positive integer monotone if it has one digit, or its digits are strictly increasing or strictly decreasing left to right (e.g. $3$ , $23578$ , $87620$ — but not $88$ , $7434$ , $23557$ ). How many monotone numbers are there?

Answer

Solution

Difficulty	7/10
Topics	combinatorics, Counting, Casework

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