data/problems/113.yml
---
:id: 113
:name: Non-bouncy numbers
:url: https://projecteuler.net/problem=113
:content: |+
Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468.
Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420.
We shall call a positive integer that is neither increasing nor decreasing a "bouncy" number; for example, 155349.
As _n_ increases, the proportion of bouncy numbers below _n_ increases such that there are only 12951 numbers below one-million that are not bouncy and only 277032 non-bouncy numbers below 10<sup>10</sup>.
How many numbers below a googol (10<sup>100</sup>) are not bouncy?