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.

The number of integers of n digits is equal to the binomial coefficient C(n,9) [OEIS A000582]. For n=10, 92378.

zero digits is represented by the digit 0: 1
1 digit (1 to 9) + 0                     : 10
2 digits + 1 digit + 0                   : 55
3 digits + 2 digits + 1 digit + 0        : 220
4 digits + 3 digits + ... + 0            : 715
5 digits + 4 digits + ... + 0            : 2002
6 digits + 5 digits + ... + 0            : 5005
7 digits + 6 digits + ... + 0            : 11440
8 digits + 7 digits + ... + 0            : 24310
9 digits + 8 digits + ... + 0            : 48620
10 digits + 9 digits + ... + 0           : 92378 <<<

Edited on December 31, 2015, 3:30 am

Posted by Dej Mar on 2015-12-30 12:43:40