Music on the planet Alpha Lyra IV consists of only two notes, called A and B. Also, songs never include three consecutive repetitions of any sequence nor does BB ever occur. A sequence of notes can have 1 or more notes in it.

What is the longest song on Alpha Lyra IV?

(In reply to re(2): Proof of Infinite Length by DJ)

Your proof may shed light on why 16 is the minimum.  Simply modifying the 0/1 system to exclude all -11-s, it is easy to see that the longest possible is the following:

110101
Neither 1 or 0 can be attached to the end, because it would add an extra B at the end of the sequence below.
BAABAABABAABABAA
A can't be attached to the beginning because ABA would repeat 3 times.  B can't be attached to the end because ABAAB would repeat 3 times.

This isn't a complete proof, but it makes it a convincing argument.

Posted by Tristan on 2004-12-16 00:41:02