A man emerged smiling from behind the tent flap. He blinked, adjusted his tunic, and sauntered off.
“Next!” Diotima called, without taking her eyes off the clock. It had only a few drops left to run. At the last drop, Diotima turned it over and made a mark on a wax tablet. She consulted her notes and said to the man at the head of the queue, “Let’s see, you’re doggy.” She handed him four obols from the stack of coins.
The man said, “But what if I want something else?”
“If you want free sex, then you do it my way,” she told him. “You’re wasting time. Get in there and stop screwing about-er.” Diotima realized what she was saying. “That is, do screw about.”
The man grinned and went inside. A moment later, we heard a brief squeal from Petale.
“Diotima!” I said, shocked.
Diotima looked up, pushed back a wisp of dark hair from her eyes, and said, “Oh, hello, Nico.”
“What in Hades do you think you’re doing?”
“We need to know how long Petale spent with clients. Didn’t I say to leave it me?”
“Petale doesn’t remember how many clients she saw.”
“I found a way to work out her payments. Most of them, anyway.”
“No one can look at a jar of coins and deduce in what handfuls they’d been put in. I know you’re smart, Diotima, but I can’t believe even you could do it.”
Diotima blushed. “I … er … had some help.”
“Who could possibly do such a thing?”
“Hi, Nico!” came a boy’s voice from under the table.
I bent to look. There was my little brother, Socrates.
“Socrates worked it out,” my wife admitted sheepishly.
“You asked a child?”
“Well, he is my brother-in-law, you know.”
“It was fun, Nico,” Socrates said eagerly as he crawled out from under the table. “A really unusual puzzle. But I solved it!”
“How?” I said, unbelieving.
“Say there are fourteen obols in the jar. Then it must be for a man on top and a doggy. Because man on top is ten obols, and doggy is four.” Socrates paused. “Er … I thought at first doggy had something to do with-you know-dogs. I wondered where they all were. It was a bit of a relief when Diotima explained about the different ways. Hey Nico, which positions do you and Diotima-”
“Can we get back to Petale?” I interrupted. “Why couldn’t it be for something else?”
“Oh, sure. Well, woman on top is nine obols, and standing is three, and there just isn’t any other way to make fourteen. That’s only an example, of course. You see?”
I saw. “That’s really quite clever. But I saw Petale’s money jar. There must more than a hundred coins.”
“Yes, Nico, but the customers come from different cities. Lots of different cities. There weren’t more than a couple of customers from each place.”
“Go on,” I said, intrigued despite myself.
“Well, every city has its own coins, and everyone paid in their own currency.”
It struck me like a hammer. “Dear Gods, Socrates, that’s brilliant!”
Socrates smiled like the rising sun. “Thanks, Nico! Do you know, I think that’s the first time you ever said I did something smart? All the other times you-”
“Don’t get carried away,” I told him. “Go on with your calculation.”
“Oh, well, in the jar there are only a handful of coins from most cities. So it’s easy to work out all the different ways they could have been paid. Lots of the solutions are obviously ridiculous; we can eliminate those.”
“And where there’s ambiguity,” Diotima added-I heard the I-told-you-so in her voice-“it usually doesn’t change how many men paid.” She shrugged. “Sometimes we took the high answer, sometimes the low. It’ll even out close enough that we know how many men she saw.”
“But the coins from different cities have different values.”
“Sure.”
“To do this you’d have to know the fees in the coins of every city in the country for every way of having sex.”
“Oh, that’s all right,” Socrates said. “I memorized them all. Petale told me all the going rates.”
Terrific. My wife was running a brothel, and my little brother had memorized the cost of every sexual position with a prostitute for every currency in Hellas.
Diotima said, “I’m timing the same number of men, duplicating the positions as close as we can get them. Pretty soon now I’ll be able to tell you what time Petale saw Arakos the Spartan.”
The answer would be a gift of the Gods, but I still had trouble believing the answer could have been divined.
“Socrates, tell me the truth, did you really work out how many men she serviced? You’re not making this up, are you?”
“No, Nico,” he said, and he sounded hurt. “I can prove it. Honest. I’ll show you every step.”
“No,” I said at once. “I believe you, Socrates. I’m sorry I asked. So how many men in all?”
His eyes and mouth became large as plates. “A lot.”
“You’ve done well. Good thinking, Socrates.”
“Thanks, Nico!” He beamed.
“Uh-don’t mention this to our father.” I pulled Diotima to the side. “You’ve been teaching Socrates about sex,” I hissed.
“He was surprisingly ignorant for a twelve-year-old,” she said calmly. “Fortunately he didn’t need to know much to solve the mathematical problem.”
“That’s not the point. I told Father you’d never be involved in prostitution. What if he finds out?”
“It’s more important to get the answer.” Diotima looked at Markos, who’d listened to all this with a bemused expression. “Who’s your friend?” she asked in a loud voice, quite blatantly changing the subject.
“Markos, meet my fiancée, Diotima. Diotima, this is Markos of Sparta.”
They looked each other up and down.
At that moment the man emerged from the tent.
“Oh!” Diotima rushed back to the table and ran her finger down the list. She grabbed a handful of coins and thrust them at the man first in line.
“She’s on top. Go!”
The man nodded his head and stepped in quickly. Diotima might not have approved of the seamier side of life, but she certainly knew how to run a brothel.
She became preoccupied with her chart, checking her figures. Markos and I looked at each other, both desperately trying not to laugh. Markos grinned and said, “Your remarkable lady would have made a fine madam.”
“I wouldn’t say that to her if you wish to live.”
“I don’t suppose Diotima has a sister, does she?”
“Sorry, Markos, you’ll have to find your own clever priestess.”
As I said it, I thought what a pity that was. I would have enjoyed having Markos for a brother-in-law.
Diotima turned her attention back to us. “What have you two learned?”
Markos and I took turns telling her what we’d been up to while Diotima listened closely. From time to time as we spoke, she had to break off the conversation to usher in another client for Petale.
When Markos and I finished, Diotima said, “Dromeus accuses Festianos and One-Eye. One-Eye accuses Dromeus. Festianos implies either Dromeus or One-Eye would have been happy to do the deed. The only person everyone agrees would not have killed Arakos is Timodemus, and he’s the one who’s arrested.”
“How do you like Uncle Festianos or One-Eye as murderers?” I asked her.
“They’d be a start.”
It occurred to me my friend Timodemus might be a trifle miffed if I saved his life but got his father or uncle executed. I said, “Why do you think Dromeus named them?”
“For the traditional reason,” Diotima said. “He hates them. But they’re all members of Timo’s team.”
“No one else has a motive,” Markos pointed out.
“Is there no one among the Spartans?” she asked. “Had this prickly pankratist no enemies at home?”
Markos considered. “It’s a reasonable question,” he conceded. “But why, if you were a Spartan, would you pick Olympia to murder a fellow citizen? Surely there’d be better opportunities. In fact, I know there are.”