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 Proof of Infinite Length by DJ)

All that is needed to disprove this argument is a simple counterexample:

Take the 16 note solution offered by Charlie and Jer.

baabaababaababaa
0110110101101011
babaabaababaabaababaababaabaababaababaabaa

As this counterexample shows, the 0/1 system has more unusable combinations than the a/b system.  As shown above, the -11- combination (dashes represent any number) is not allowed.  I wouldn't be surprised if there were other combinations not allowed in the 0/1 system.

Excellent thoughts!

Posted by Tristan on 2004-12-15 04:51:45