perplexus.info :: General : String length differences

String length differences (Posted on 2005-02-15)

Consider the sequence 0100111100
There are 5 zeroes and 5 ones in this sequence.
The longest string of ones is 4.
The longest string of zeroes is 2.
The difference in string lengths is 2.

Create a sequence consisting of 100 zeroes and 100 ones which maximizes the difference in lengths between the longest string of 1's and the longest string of 0's.

Find a formula for the maximum difference in string lengths with n zeroes and n ones.

Submitted by Jer

Rating: 4.0000 (3 votes)

Solution: (Hide)

With 100 of each the greatest difference is 82. There are 10 strings of 10 zeroes interspersed with 8 single ones and a single string of 92 ones.
The formula for the second part is int(x+2-2sqrt(x)) which I can't seem to give a good proof of.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-06-23 02:03:17
solution	rajeshkumar	2005-02-20 07:53:35
Without peeking	Larry	2005-02-17 21:01:07
Solution to part 1	Steve Herman	2005-02-15 15:27:17
solution	Charlie	2005-02-15 15:23:00

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