## Problem of the Day #366: Canyon NumbersMarch 19, 2012

Posted by Alex in : potd , trackback

Today is MPotD’s one year anniversary! A canyon number is a number with at least three digits that satisfies the following properties:

1. The first and the last digit are the same.
2. There is a unique minimum digit, $k$.
3. The digits up to and including $k$ form a strictly decreasing sequence.
4. The digits including $k$ and beyond form a strictly increasing sequence.

Find the number of $10$-digit canyon numbers.