ARGH. So this was a casualty of the move to Google. I thought I saved all the pieces I'd written, but this one was apparently left behind. Fortunately, I have it written down, but I don't have all the notes.
While doing research for Mathematics in Historical Context, I came across a work by Alcuin titled Problems to Sharpen the Minds of Youth. It included a number of problems, some mathematical, many logical, and I came across one (you'll know which) that meant I absolutely had to write a song about it. From a purely objective viewpoint (mine, in other words), this song is far superior to the other riddle song, the one about cherries and stuff.
Somewhat later, while doing research for my story about Odysseus and Achilles, I discovered something else. After Odysseus's death, his widow Penelope married Telegonus (who was actually the one who killed Odysseus, though in a typically Greek tragic fashion..), and Telegonus's mother Circe married Penelope's son Telemachus...
The music is Chestnut (from Playford).
Once a wise man said to me that if a learned lad I should be I must learn to count and write and answer give to these questions. "Plow seven furlongs with four oxen strong standing thirteen hands on a summer's day. Count if you can the footprints left by the oxen in the furrows made along the way. Next tell me this how shall virtue preserve when three couples come to a river's side When they must use a little boat that will surely sink if three of them should try to ride." Spoken: Let's think upon this...ah! "Footprints none the oxen leave, the plow erases every trace." Then I showed him how to cross to leave each good wife's good name in place. "Clever you are!" said the man with a smile, "Now turn all your wits to this last request. Solve this conundrum that has vex'd lawyers, bishops and some dukes and knights out in the west. Jack married Kate and then her daughter Bess soon Jack's father John called her own man. Each happy couple had a son, tell me what the two boys call each other in this clan." Spoken: Jack married Kate, and her daughter married his father, so... "Since Kate's daughter wed Jack's dad, then Bess is mother to Jack as well. Jack's his own grandfather, too, his father John the same tale may tell. Jack's newborn son has for sister Jack' mom, so to Jack his son is his father too. Jack's father's son is brother to Jack himself so he can call Jack's son his own nephew. But don't forget that Jack's dad is his son, so Jack's son is brother to grandfather. Thus climbing up this family tree it is plain to see that each is nephew to the other."
This problem is often referred to as the jealous couples problem: Three couples come to a river, and the boat can only take two across at a time. The husbands are mutually jealous, and will not permit any woman to be in the boat or on the shore with another man, unless her husband is also there. How can they cross the river? There are thousands of variations.
This is actually the reason I wrote the song. A few of Alcuin's problems are of the so-called "strange families", and except for giving the individuals names, this is exactly the situation and solution given by Alcuin (without the reasoning, and Alcuin disregarded the possibility of Jack and John being their own grandfathers).
At the 2010 Bardic Champions, I made it to the final round (after telling the story of Hermes and Argus, and singing The Farmer and the Gun). The rules for this competition were that each finalist had to submit a resume listing what they could do, and the King and Queen would decide what they wanted to hear. If anybody's listening, I think that was a great idea and should be retained in future championships.
I was given the option of storytelling or singing, with the limitation of "Under 3 minutes" (apparently, I talk too much...again, see Hermes and Argus...it was going to be 2 minutes, but one of the judges convinced the king to raise the limit to 3). This was a problem, because I'd never timed any of my stuff...the other pieces I'd prepared were The SCA Parents Song (if the request was for SCA filk), the Odysseus and Achilles story (for European stories, told by William), the rat story (for Japanese stories, told by Fujimoto), and What if I Never Speed (for period music). I knew the Odysseus story was well over 3 minutes, and wasn't quite happy with my period music. It ended up being a toss-up between the SCA Parents song and this one. I ended up choosing this one because I didn't want to do SCA filk and break the perioid atmosphere. Oddly enough, it would have been easier if the limit had been 2 minutes, because the only thing that was under 2 minutes was the rat story.