How many positive integers are there whose digits strictly increase from left to right?

Guest Apr 13, 2020

#1

#5**+1 **

**For example: 123 is the smallest 3 digit integer with digits strictly increasing left to right.**

*We list smallest numbers like cases in the example:*

*1 (does not count)*

*12*

*123*

*1234*

*12345*

*123456*

*1234567*

*12345678*

*123456789*

Notice how for each of these cases. The number with \(n\) digits has \(10-n\) cases that fit the problem. Starting with the two digit numbers, the number of cases that fit the problem is 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = \(\boxed{36}\)

I'm not sure if this is correct, but it is my attempt on the problem.

AnExtremelyLongName
Apr 13, 2020