We Got A Problem #3: ABACAB

The Genesis song “Abacab” was named after the original order of its sections: A-B-A-C-A-B.  Poetry rhyme schemes use the same convention: the rhyme scheme for a limerick is AABBA.

How many rhyme schemes are there for six-line poems?  ABACAB is one of them.  So are AAAAAA and ABCDEF.

(The fine print: if a new line doesn’t rhyme with any previous line, it must use the next available letter in the alphabet.  BAAB is wrong: it should have been ABBA. ABACAF is wrong too.  The first letter is always A.)

We’d love for readers to be able to explore this problem, so resist the urge to provide answers in the comments. Instead, we’d love helpful suggestions and ideas about different ways to approach the problem, successful or not. If you’d like to provide a full solution, do so with a pingback to your own blog!


About Bowen Kerins
Bowen is a mathematics curriculum writer. He is a lead author of CME Project, a high school curriculum focused on mathematical habits of mind, and part of the author team of the Illustrative Mathematics curriculum series. Bowen leads professional development nationally, primarily on how math content can be taught with a focus on higher-level goals. Bowen is also a champion pinball player and once won $1,000 for knowing the number of degrees in a right angle.

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