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Increasing and Decreasing Numbers

eddybob123

Active member
Aug 18, 2013
76
Intended for high school students:
Let a positive integer be called "increasing" if every one of its digits is strictly greater than the one directly to the left of it. For example, 289 is increasing but 6788 is not.
How much 3 digit increasing numbers are there?
How much 4 digit increasing numbers are there?
How much n digit increasing numbers are there?
(Note: a number can't start with 0.)
Likewise, call a number "decreasing" if every digit is less than the digit directly to the left of it.
How much n digit decreasing numbers are there?