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Problem of the Day #366: Canyon Numbers March 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.

Comments»

1. EqualRights! No Corruptions! - April 5, 2012

This is racist to valley numbers, which aren’t as big in magnitude as canyon numbers. Also, these canyon numbers are the rivals of mountain numbers..

123454321 Mtn. Number
543212345 Cnyn. Number
–> See how not well they get along, practically at eachtoehrs throughts..