For how many integers having between 1 and 10 digits (base 10) are all of their digits when read from left to right monotonically increasing? In other words, every digit is less than or equal to all of those to its right. For example, 244467889 is one of them, and 0 is another, but there are more.

sum for C(8+m,8) for m from 0 to 10
comes out to 92,378

counts zero as a zero digit number.  The 8 seems to be because without leading zero there are 9 choices of digit but if the second matches the first it become identical to having one digit fewer.

While I am not completely sure this is correct, I highly doubt a number over 600,000,000 can be right because I doubt that anywhere near 60% of numbers are monotonously increasing.

Posted by Jer on 2015-12-30 12:57:55