Problem 113
Non-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.
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?
非弹跳数
从左往右，如果每一位数字都大于等于其左边的数字，这样的数被称为上升数，比如134468。
同样地，如果每一位数字都大于等于其右边的数字，这样的数被称为下降数，比如66420。
如果一个正整数既不是上升数也不是下降数，我们就称之为“弹跳”数，比如155349。
随着n的增长，小于n的弹跳数的比例也随之增长；在小于一百万的数中，只有12951个非弹跳数，而小于1010的数中只有277032个非弹跳数。
在小于一古戈尔（10100）的数中有多少个非弹跳数？