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.

(In reply to

solution, starting out with analytic by Charlie)

**I AGREE -** the correct answer is** **__92378__

My solution started by 9,45,165... and later identifying the summation of PASCAL'S TRIANGLE diagonal rows.

On the web I have found an interesting mapping of monotonously increasing numbers into a binary number, however it is not applicable for large numbers, due to "virtual counter" limitations.

Spent significant amount of time, had fun.

*Edited on ***December 30, 2015, 3:43 pm**