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Inflationary Sequence

At a mathematics conference recently, I picked up an interesting problems from one of the speakers (C.B., CWU).

Problem: How many positive integers have the property that their digits increase as read from left to right? Some examples of such numbers are 19 or 356 or 12,679.


Hint: Some possibilities:

  • Can any digits repeat?
  • Try a smaller case...Say using the digits 1-5...is there a pattern involved?
  • Find an "intuitive" straight-forward way to solve the problem...


Solution Commentary: Another hint of sorts....first write down the special number 123456789. Any number in our sequence is "hidden" in this special number, just by crossing out some of the other digits. So, how many ways can you chose a subset of the digits of this special number...or how many ways to cross out some of the digits?

Hope this enough to get you re-started on the problem....