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

Home > Numbers > Sequences
At least 3 zeroes (Posted on 2018-10-03) Difficulty: 3 of 5
How many binary strings of length n, having three or more zeroes, exist?

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution A different assumption | Comment 4 of 5 |
The solution given so far, 2^n - n(n+1)/2 - 1, assumes that a binary string can begin with a zero.

I choose to assume that all binary strings except for 0 must begin with a 1.  Under this assumption, we can apply the same formula to the string of (n-1) digits after the leading 1.  This gives a solution of 
2^(n-1) - n(n-1)/2 - 1.  This formula works even when n = 1.

  Posted by Steve Herman on 2018-10-03 16:39:16
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 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information