# Problem 112: Bouncy numbers
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. Clearly there cannot be any bouncy numbers below
one-hundred, but just over half of the numbers below one-thousand (525)
are bouncy. In fact, the least number for which the proportion of bouncy
numbers first reaches 50% is 538. Surprisingly, bouncy numbers become
more and more common and by the time we reach 21780 the proportion of
bouncy numbers is equal to 90%. Find the least number for which the
proportion of bouncy numbers is exactly 99%.