Illustration by Marc RosenthalFrom the forthcoming book Dr. Broth and Ollie's Brain-Boggling Search for the Lost Luggage by Michael Abrams and Jeffrey Winters. Illustrations copyright © 2000 by Marc Rosenthal. To be published by Fireside/Simon & Schuster, Inc. Reprinted by permission.
Dr. Broth, professor emeritus of non-Euclidean paleolinguistic astrohistoriography, has lost his luggage— and along with it, his manuscript on indopithecine tribal kinship equations. Aided by Ollie, a topiary-tending gardener, and McGuffin, a time-traveling alpaca, Broth has been traipsing about the universe in search of his luggage. In an earlier encounter, the comrades learned that the luggage was heading toward India, but, as you will see, while McGuffin can transport the trio to the right time or place, the alpaca rarely manages both. . . .
Once Upon a Prime in Italy
"Need I point out," said Dr. Broth as some girls in togas passed by, "that this hardly appears to be 21st-century India?"
"What do you mean?" said McGuffin, gazing at the urns the girls carried. "Looks like I've taken you to the biggest toga party in the history of Rajasthan State University."
"Perhaps it's not altogether a surprise," said Broth. "We forgot to factor in continental drift."
The flat, dusty land spread out for miles until it collided with a clump of small mountains. On a narrow path leading up into the hills, a lanky disheveled man appeared, heading their way. They could make out a long unkempt mustache, ragged clothes, and a tall wide-brimmed hat.
 |
"As a matter of fact, yes," said Dr. Broth. "Do you know what century it is and how we might be able to get out of it?"
"It just so happens that I was ponderin' on that problem this mornin'. Seems like everyone's got their own ideas about it. Back where I come from, people think one thing; but here, they think another. Up north, it's altogether a different story. And those Persians, who think they're something big, they got ideas altogether their own. Personally, I figure time's been going on forever and'll keep on going on forever, so why put too fine a point on it?"
"Perhaps you could tell us," asked Ollie, "who the current king of Rome is?"
"Why, sure. Lucius Tarquinius Superbus. Superbus, I assure you, is just a name."
"That puts us in the sixth century B.C.," said Dr. Broth.
"I see y'all're number-minded folk, yerselves. Can't help noticing that there's three of ya. Three's the first proper pyramid number, and a very masculine number, too. It's no coincidence that yer all of the male persuasion."
"Just my bad luck," said McGuffin, still looking at the passing maidens. "Could you get me some of those babes' numbers instead?"
"If yer interested," continued the man, "I'm headed to Croton, where I happen to be high sheriff. We're about to start our own Olympics, a kinda number Olympics. Thought we'd put up a little competition to the muscle games. If y'all got a mind fer it, maybe y'all can come compete."
"I've always wanted to see how I'd compare to the best minds of ancient Greece and Rome," said Dr. Broth. "Who knows? Maybe we'll meet Pythagoras or some other genius."
"Pythagoras: that's ma name— don't wear it out! If y'all have come to join my colony yer in luck. Croton's just a hop and a holler away." After following Pythagoras, high sheriff of Croton, for several hours, they came upon a fortress. A gigantic flag depicting five interlocking circles hung from its outer wall.
"Look, it's the sign of the Olympics," said McGuffin.
"That's our first contest," said Pythagoras. "Everyone should be working hard on it right now. The idea is to fill every section made by the circles with a number from 1 to 15. The numbers in each circle should add up to a prime number. Then, if it so happens ya can get that far, add up the sum of each circle to get the highest number possible, and that's how we find our winner."
"Why, this is a simple Venn diagram," said Dr. Broth. "But the introduction of cortatras to this selection of integers creates a complication. In fact, while there's a finite solution, finding it could require advance— "
"I think," said Ollie, humbly, "I see a winning answer."
The Principles of Seating
"That about settles that," said Pythagoras suspiciously. "You may want to stick around for the rest of the competition."
Thousands of people were flocking to the compound, many dressed in togas and a few in robes lined with purple. Pythagoras ushered the crew inside the walls to a great stadium, which was quickly filling up. He invited them to sit on the stage among the circle of competitors.
 |
"There are two kinds of judges," explained Pythagoras, "the Stoics and the Dionysians. Four of each must sit in the front row. But the Dionysians love diversity and prefer to sit behind one Dionysian and one Stoic. The Stoics, on the other hand, prefer homogeneity and will sit only behind two Stoics or two Dionysians. Aside from the eight judges in the front, there are 11 Stoics and 17 Dionysians."
Ollie pondered the problem for a moment.
"There are two configurations that will allow all the judges to have a seat. Naturally, they're determined by those in the first row."
Ordering Off the Menu
When every seat in the amphitheater was taken, Pythagoras motioned for quiet and gave an introductory speech. "And before we begin, let me remind y'all that these numbers are the purest and most spiritual path we can take. Life on this here planet, and elsewhere in the universe, is eternal, and we must always focus on purity. The prime numbers, amigos, are the purest of all numbers. And so, before we begin this most spiritual of contests, let us take a moment to remember the 17 forbidden foods."
 |
"We shall not eat meat of any kind.
"We shall not eat lima beans.
"We shall not eat foods that have been boiled and then roasted.
"We shall not eat pinto beans.
"We shall not eat from a whole loaf of bread.
"We shall not eat kidney beans.
"We shall not eat scrambled eggs.
"We shall not eat garbanzo beans.
"We shall not eat boiled eggs.
"We shall not eat black beans.
"We shall not eat roasted eggs.
"We shall not eat green beans.
"We most definitely shall not eat eggs that have been boiled and then roasted.
"We shall not eat string beans.
"We shall not eat any food that causes flatulence.
"We shall not eat baked beans.
"We shall not eat beans of any kind."
"It's hardly a coincidence, my brothers and sisters, that there are 17 forbidden foods. Seventeen is the most divine of all primes. And now for our first ceremonial competition."
A slave in a purple toga brought Pythagoras the frames of three triangles. "These triangles," he explained, "must be arranged, by placing them on top of one another, so that 17 sections— representing, of course, places for the 17 forbidden foods— are made by their intersections."
"I don't see how that could possibly . . . ," started Dr. Broth, glancing over at Ollie's wax tablet. Ollie was putting the finishing touches on his sketch of the solution.
Solution
Want to see the solution to this puzzle?
Got new solutions for the puzzle? Want to see other people's solutions? Talk to the puzzle master in his discussion forum at www.scottkim.com.
