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Comments on Place numbers around a circle to make all length 3 binary strings.

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Place numbers around a circle to make all length 3 binary strings. Question

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There are 8 binary strings of length 3.

They are:

000
001
010
011
100
101
110
111

The goal of this puzzle is to arrange some 0’s and some 1’s around a circle (using as few 0’s and 1’s as possible) so that all 8 binary strings listed above appear at least once around the circle.

A binary string is considered to appear around the circle if the 3 numbers of the binary string are located in three consecutive clockwise positions around the circle.

In the example below, the binary string 110 appears starting at the 1 marked with a star. But the binary string 101 does not appear anywhere.

5 numbers arranged around a circle.  Starting clockwise from the top, they are 0, 1*, 1, 0, 0

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1 comment thread

Presumably you want the optimal solution, with the fewest numbers. This is just a de Bruijn sequence.... (2 comments)
Presumably you want the optimal solution, with the fewest numbers. This is just a de Bruijn sequence....
Moshi‭ wrote 7 months ago

Presumably you want the optimal solution, with the fewest numbers. This is just a de Bruijn sequence. The Wikipedia article has one for length-3 binary strings.

You’re right. Please feel free to post this information with an actual example as an answer.