This question is about Project Euler 113:
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 10^10.
How many numbers below a googol (10 pow 100) are not bouncy?
This is obviously not something you can brute force. I found a mathematical solution that does the trick in no time, the problem is, I don't understand it!
Can someone point me in the right direction? Not having a math background, I'm not even sure where to begin!