Diophantus of Alexandria lived in the 3rd century AD and is sometimes called “the father of Algebra.” Limericks are five-line humorous poems with a strict rhyming form AABBA, invented in the 19th century and named after an Irish county. How could the two be possibly related? Well, in the following old British puzzle rhyme, for one:

1.

A beery old boozer named Button

Ate ninety-four pence worth of mutton

Each chop cost seven,

Each cutlet eleven,

How much did he eat, the old glutton?

The name of Diophantus is associated with problems whose solutions are whole numbers, such as the number of mutton chops and cutlets in the above puzzle. (You can use cents instead of pence, and I thought of changing the chops and cutlets to hot dogs and hamburgers, but having enjoyed many a tasty mutton chop and cutlet, I decided to let the authentic flavor stand. Ahh, mutton… Hyderabadi biriyani or Trinidadian curry goat, anyone?).

But back to Diophantus. So strongly was the name of Diophantus associated with puzzling and poetry that his epitaph apparently reads:

2.

Here lies Diophantus, the wonder behold

Through art algebraic, the stone tells how old

God gave him his boyhood one-sixth of his life,

One-twelfth more as youth while whiskers grew rife

And then yet one-seventh ere marriage begun;

In five years there came a bouncing new son.

Alas, this dear child of master and sage,

Attained only half of his father’s age.

When chill fate took him. An event full of tears –

Heartbroken, his father lived just four more years.

Since the poem is in English, it’s obviously not authentic, and what’s more, I’ve modified the last part to make it rhyme. If you examine it closely, it admits of two interpretations. Only one of these is the official Diophantine solution (where his life lasted a whole number of years): the other is not. Can you figure out both solutions?

Here’s one from Arabia, about the camel fortune of a Bedouin merchant:

3.

Bezout acquired nineteen camels through his trading skill,

“Of the collected camels,” it said in the late merchant’s will,

“Exactly half go to my first son, Abdul,

One-fourth to Wasim, one-fifth to Rasul,

Call a wise man to distribute — don’t sell or kill.”

The sons couldn’t figure out how to divide the camels and consulted the local wise man Al Khw’izmi, who promptly solved their problem. How did he do it?

Here’s a final Diophantine limerick for our math whizzes.

4.

A small little equation do I satisfy,

Add 24 times x to 36 times a different y,

The equation sure is Diophantine,

And x and y could be either sign

I’m positive the smallest such one am I

Can you explore and generalize this problem?

The literary challenge this week, of course, is to come up with a Diophantine limerick or poem. If inventing math problems is not your forte, consider this classic limerick by Ogden Nash:

A daring young miss from Connecticut

Once flagged the express with her pecticut,

Which critics defined

As presence of mind,

But deplorable absence of ecticut.

This uses a literary device, the “puzzle rhyme,” that has been well executed in some limericks. You end the first line with a place name that is pronounced differently from the way it is spelt. Then you spell creatively rhyming words or phrases the same way in lines two and five, so they become mini-puzzles for the reader to solve. The above example’s quite dated: a modern teenager will probably have trouble figuring out what a “pecticut” is, and will then wonder why it was necessary. So how about some original modern examples?

As usual, you can submit answers as comments here. Don’t be shy about submitting answers to any of the problems: you don’t have to address them all in one comment. The weekly prize, a copy of “Mathematical Puzzles of Sam Loyd” (edited by Martin Gardner), will go to someone who comes up with an especially interesting answer or to someone who proposes a sufficiently intriguing puzzle for Lab readers to solve. (To submit a puzzle, send an email message with “NEW LAB PUZZLE” in the subject line to tierneylab@nytimes.com. Please include the solution to the puzzle and indicate whether or not the puzzle is original.)

Happy puzzling and remember – if you can’t do any better, you can always do verse!

Comments are no longer being accepted.