Let's call n an ascending number, if it has the following 2 properties:

- The number n has at least 2 digits.
- All digits of n are in ascending order, in base 10.

How many ascending numbers are there?

(In reply to solution by Charlie)

That is a stunning answer Charlie. The beauty is in the simplicity.

Though, for sake for completion, I do think one must take a view on whether the problem, as stated, allows the legitimate use of leading zeros or not, rather than leave it at two optional answers.

Personally, I think leading zeros not only can, but must be used. So the answer, according to me, would be a definite '1013' and not a conditional '502 or 1013', depending on whether we want to consider leading zeros or not.

I guess it boils down to whether, for example, we can consider 012 and 12 as different 'numbers' or not. I believe they are different numbers (one is a two digit number and the other is a three digit number) with the same quantitative value rather than being the 'same' number.

Posted by Sanjay on 2003-05-25 07:17:08