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

Home > Numbers
Digitally Average Integers (Posted on 2019-08-14) Difficulty: 3 of 5
We will say that an integer is digitally average if the average of its (decimal) digits is 4.5 (the average of the digits from 0 to 9). How many 10-digit integers are digitally average?

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
solution | Comment 1 of 2
we can use generating functions to solve this problem.  If we allowed leading zeros then we could simply use the coefficient of x^45 from the expansion of (1+x+x^2+...+x^9)^10 which turns out to be 432457640.  To eliminate those which have leading zeros we can subtract the coefficient of x^45 from (1+x+x^2+...+x^9)^9 which is 40051495.

Subtracting these two we get
432457640-40051495=392406145

so there are 392,406,145 such 10-digit numbers

  Posted by Daniel on 2019-08-14 08:41:31
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 (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information