Almost, just almost

Probability Level 4

We say that a number is almost increasing if for each digit of that number, either that digit is 0 or all digits to the left of it are (strictly) smaller than it. How many 4 digit numbers are almost increasing?

Details and assumptions

As an explicit example, the number 20352035 is almost increasing.

The number 12=01212=012 is a 2 digit number, not a 3 digit number.


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