All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Monotonous integers (Posted on 2015-12-30) Difficulty: 3 of 5
For how many integers having between 1 and 10 digits (base 10) are all of their digits when read from left to right monotonically increasing? In other words, every digit is less than or equal to all of those to its right. For example, 244467889 is one of them, and 0 is another, but there are more.

See The Solution Submitted by Steve Herman    
Rating: 1.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution answer | Comment 1 of 9
The number of integers of n digits is equal to the binomial coefficient C(n,9) [OEIS A000582]. For n=10, 92378.

zero digits is represented by the digit 0: 1
1 digit (1 to 9) + 0                     : 10
2 digits + 1 digit + 0                   : 55
3 digits + 2 digits + 1 digit + 0        : 220
4 digits + 3 digits + ... + 0            : 715
5 digits + 4 digits + ... + 0            : 2002
6 digits + 5 digits + ... + 0            : 5005
7 digits + 6 digits + ... + 0            : 11440
8 digits + 7 digits + ... + 0            : 24310
9 digits + 8 digits + ... + 0            : 48620
10 digits + 9 digits + ... + 0           : 92378 <<<

Edited on December 31, 2015, 3:30 am
  Posted by Dej Mar on 2015-12-30 12:43:40

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (7)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information