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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    
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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
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