Steven G
Elite Member
- Joined
- Dec 30, 2014
- Messages
- 14,383
I am having a great deal of trouble getting a handle on this problem.
Let x be in N. We call x nice if it is bigger than 10 and its decimal representation x = (ak, ... , a1) has the property that
ai+1 < ai for all 1 < i < k. For example 34 = (3, 4), 126 = (1, 2, 6) are nice while 3 = (3), 76 = (7, 6) are not. How
many nice numbers bigger than 10^5 are there?
I realized the 6 digit numbers go from 123,456 to 456,789
The 7 digit numbers go from 1,234,567 to 3,456,789
8 digits from 12,345,678 to 23,456,789
9 digits from 123,456,789 to 123,456,789
I can count these but in the worst way possible. I was hoping for a cleaner way to do this problem.
Thanks!
Let x be in N. We call x nice if it is bigger than 10 and its decimal representation x = (ak, ... , a1) has the property that
ai+1 < ai for all 1 < i < k. For example 34 = (3, 4), 126 = (1, 2, 6) are nice while 3 = (3), 76 = (7, 6) are not. How
many nice numbers bigger than 10^5 are there?
I realized the 6 digit numbers go from 123,456 to 456,789
The 7 digit numbers go from 1,234,567 to 3,456,789
8 digits from 12,345,678 to 23,456,789
9 digits from 123,456,789 to 123,456,789
I can count these but in the worst way possible. I was hoping for a cleaner way to do this problem.
Thanks!