Non-bouncy numbers
Problem 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 1010.
How many numbers below a googol (10100) are not bouncy?
from tools import combinations
def run():
num_of_diggits = 100
return combinations(10 + num_of_diggits, 10) + combinations(10 + num_of_diggits - 1, 9) - 10 * num_of_diggits - 2