Chapter Prime and Sum of Three Primes
Scene Two: Magic Square
In his room for only half an hour, Den unfurled the letter from Carinde. He flattened it. His hands found a few things on his desk – a compass, a penny, a quill – to hold down the edges. Then he stared at the parchment and wondered how it had beaten him to Oupenli.
There was no sign of the text being re-written. Sometimes there wasn’t one when magic was involved. He didn’t want to cast numeromancy in an attempt to discover clues. Among the many problems with that, his amateur magic could mar the fine line drawings or colors. Cari had measured her angles to make a sixteen-point moravian star. There were trace marks and a pale 22 1/2 in the margin. Below the sketch was the footnote, “Here is a shining star. It is my sixteenth. 360 does not divide evenly by 16. But nearly.” Den didn't want to ruin any of it.
Her notes, especially her questions, seemed so insightful that he began his reply immediately. His fingers kept transcribing his never-ending thoughts about her thoughts, one after another, until his hand cramped. After that, he took a break from writing, read her letter a second time, and got up to re-pack his bags so that they would fit on a coach. He rested on his cot until the innkeeper’s nephew rapped on the door of his room and announced dinner.
“Better hurry,” the young man said. “A teamster off of the street just walked in and said that he’ll drink all of the beer we’ve got.”
“Not eat all the food?”
Den rolled off of his cot. “Plenty of time.”
He had determined to stay out of trouble until he checked the coach schedule. The earliest he could do that was in the morning. Probably it would be wise to stay out of trouble forever more, too, or at least for the rest of his time in Oupenli. He’d have to be patient for a couple of days here unless there was an immediate opening on the next coach, an unlikely event.
Downstairs at the common tables, he choose the seat in the corner section between the fire and the bar. No one would find it easy to talk to him here. As an extra precaution against unwanted companions, he brought his book of math lessons. Nothing shut up non-accountants like seeing a few equations. While he sipped a pint of the inn’s clear ale, he flipped the pages. Mentally he reviewed the lessons he had given to Carinde in person and in letters so that he could decide what the next one should be.
Three pints later, his meal arrived. It was horse steak with carrots. He’d forgotten that horse could be a dinner option after so much time in the Mundredi towns. They had no horses in the valleys, much less surplus ones. He must’ve smiled at the taste because a bald man at the bar, perhaps a wheelwright from the tools at his belt said, “Good, is it?”
Denario held his book up higher in front of his face. He wished the book cover had much bigger equations written on it that no one could possibly miss seeing.
By the end of his fourth pint, a monk joined the slurping, lip-smacking, supper crowd. He wore a brown robe. When he took a seat at the bar, he removed a book and a pointy hat from under his arm. He placed them on the counter top. His hair was brown. His beard was golden. He looked young for a holy man although, of course, they all had to start out at some age or other. Den glanced at the hat. It had geometric symbols on it. It came to a point. The monk had a wizard’s hat.
He was a wizard.
Den raised his book again. The wizard noticed, smiled, and waggled his little tome right back. The accountant had a moment to think. This was the drunk who the bank wizard had consulted in the middle of the marketplace in front of the Agrabar embassy. He had changed his robe and had sobered up as he slept all day, but it was him.
Cautiously, Den smiled. The fellow nodded once and, even better, proceeded to ignore the accountant and everyone else in favor of the nearest keg. He told the barkeep he wanted the usual and that man grunted and tapped the keg into a bowl of wine. He began stirring.
When Denario next glanced up from his page, he saw the wizard drinking his mix of beer and red wine from a goblet. With his free hand, the blonde fellow turned over his book. He slipped. He picked up the book. He turned it upside down. His head craned back for another swig. His hands fell to the leather-bound volume and tried to pry open the cover.
The wizard threw the book down onto the counter. He drank more. He noticed Denario staring at him and he glared. Den hid behind his math lessons.
A few minutes later, Den traced a binomial equation on his table using a beer-wet fingertip. He multiplied the equation by itself, wrote the coefficients, performed the operation a third time, and watched the pattern take shape. The coefficients in the third and fourth levels were equal to the sum of the coefficients in the levels above. But his thoughts about patterns were interrupted by a bang. He jumped, half a second after the wizard slammed his book onto the counter. Still that man could not open his green cover.
“Another!” he yelled to the bartender.
The stocky local fellow reached down for a clay amphora of wine, with which he would presumably refill the bowl. He flipped it onto the counter next to the wizard.
“Need help with your book, sir?” he asked.
“Not unless you know magic squares.”
The barkeep shrugged. Lightly, he poured from the fifty-pound clay vessel into his drink mixing bowl. He didn’t spill a drop of the ruby liquid. The wizard tossed him a brasser.
Den spotted a design on the green, ox-hide cover of the occult publication. It was a diagram that was meant to represent a sliding puzzle. It had only three numbers to a side and of course one piece was missing. In a real puzzle like the ones made by masons or carpenters as toys for children, a missing spot was needed to allow the pieces to slide.
This one was merely an ink drawing. Maybe the drawing was a clue about how one was supposed to open the book.
“It’s got to be a magic square,” the wizard muttered.
“Not in that sketch,” Denario blurted. Then he covered his mouth.
The wizard looked up. He didn’t seem surprised, just impatient. He shook his head.
“Look, the numbers move.” With a grubby forefinger, he touched the 4 in the lower right corner. He appeared to push it up one slot into the empty space. Just as in a real sliding puzzle, the blank spot emerged in what had been the four space. The ink sketch might as well of been a mechanism made of clay tiles or of wood. “I know how these things work. The cover won’t open until I hit the right sequence. I have tried all of the numbers in order. I’ve tried them in backwards order. Now I’m sure it has got to be a magic square. But I daydreamed through that in school. I can’t remember how the things are supposed to work.”
“Right,” said Den, glad to see a quick end the conversation. “For a magic square, just put the tiles in order so that they sum up to the same amount in every direction.”
Den had already returned to his own book. He glanced up. He didn’t feel the need to say anything more. No sense in encouraging a drunkard.
He tried to ignore the young fellow across from him while the man, in a not-very-coordinated fashion, fumbled with his magical diagram, sighed, and drank.
Fidget, sigh, drink. Drink, drink, sigh. Fidget, fidget, sigh. Drink. Drink, drink, drink. Sigh.
“Oh, stop! Give it.” Den slammed down his own book, although not too hard because it was expensive. His left hand shot out, palm up. “It’s not going to release a demon to eat me or anything, is it?”
“Books hardly ever do.” A smile emerged in the scraggly beard. In a second, it faded, replaced by a look of caution. The wizard placed his book face up on the counter. He nudged it toward Den. “Are you in the trade?”
Den must have raised an eyebrow at the question.
“I mean, are you a professional in the magical arts?”
“I am an accountant.” Denario spoke proudly as he dodged the question.
He put his finger on the 4 tile and moved it back. The wizard had been progressing in the wrong direction. Den remembered his old ideas about how to solve these puzzles. When he was eleven, he developed of formula about how to start them.
The total per added row or column = (number of rows)((highest number + lowest number)/2)
= 3((8+ 0)/2)
So the total that he needed to arrange for every row and column was 12. Den started to move the illustrated tiles. But his gestures were impatient. He was making mistakes. Sometimes he had to backtrack. His fingers sped up. They slowed down. He had to pause to consider the next stage. Across from him, the wizard cleared his throat.
“Aha!” exclaimed Den as he realized the next sequence of moves he needed to make. With relief, he sped up again and the moving digits started to feel more natural to his fingertips. They hummed with every touch.
A second after he reached the end, the soft magic square began to glow. Denario dropped the book onto the tabletop based on the idea that glowing things were not safe. Anyway, he was finished. The wizard's left hand reached out over the book and it disappeared. It did not get blocked from sight. It did not go into a pocket in the wizard's robe. It faded.
“That was amazing,“ the wizard said.
“What I did or you?” Den paused. He was impressed by the trick of the disappearing book. “All I did was a little math.“
“Math is amazing to those of us who didn't have the patience to learn it. But anyway, that wasn't what I meant.” The wizard rubbed his thin beard. “The tiles moved for you. That’s the thing.”
“They moved for you first.”
“They are hand drawn. They are bits of ink. They don’t move for most people. You have to have experience with magic.”
“I’m an accountant,” Denario repeated.
The wizard looked around. Behind him, four men had started to shout over a game of dice. It added to the noise of twenty or so conversations. To the right, a boy who might have been the owner’s grandson stoked the common fire with sticks. To the left, the bartender mistook the pause and the wizard’s gesture. He assumed that his steadiest customer wanted more wine and beer. In a blink, he plucked up pre-mixed bowl and used it to top off the goblet while it wavered in the wizard’s grasp above the bar.
“Right, then. “ The wizard didn’t say thank you but he gave the bartender a delighted smile before he returned to his conversation with the accountant. “What do you want?“
“What a strange question. No one ever asks me what I want.” Denario looked down at his book. He was thinking of two people, Carinde and Shekel. “I suppose I want to see my apprentices.”
“No, I mean for doing the magic, the numeromancy.”
Den closed his eyes for a moment. There was a guild rate for what he had just done but it didn’t seem appropriate. He wasn’t sure it was right to charge.
“Who knows?" He shrugged. He waved his arm at the where the book had gone missing. “There was no spell I had to cast.”
“Come on, now. Most knowlessmen take the opportunity to ask for a favor.”
Maybe it was the term ‘knowlessmen.’ Den had forgotten that experts in one profession talked down to others. In the Mundredi lands, he had seldom heard that tone. Perhaps he had been spared the worst of it for a few months by belonging to such an unusual profession, one that no one felt compelled to compete with.
“I’m really trying to read,” he said. He put his hands and his book into his lap. “I'd like to do that.”
"Everyone asks for a spell. Do some magic, they say.” The wizard rolled his eyes.
“And write. I’m sure you are familiar with reading and writing.”
“I am.” The fellow seemed to have picked up on Den’s attitude at last. It didn’t dissuade him. He leaned closer. “And I know that not many people come to a bar for either of them.”
“This is not a bar. It is the commons room at my inn. Where I am staying.” He indicated the other customers with his steak knife. Then he pointed to his steak. “I am eating my dinner.”
“But you are at the bar.”
Denario glanced to his left. He was sitting three feet from the bartender.
“I am having a small drink as well.” He sat up a little taller. He set his lesson book out and re-opened it to not quite where he had left off. “It is allowed for accountants. Also, I am not the only one who brought a book to the bar. Half of the men at this bar have done it. Apparently, it is a popular thing to do. I am reading mine, you may notice.”
“Huh." The wizard swiveled around, trying to judge who was close to the bar. It wasn't hard to do the sums, surely, but he was tipsy. "Not me, as far as reading. That means half of the readers aren't doing it actually. They’re being sociable. Properly sociable.”
“Hmm.” He chewed on a bit of fat and gristle.
“I confess, I was not expecting to have a chance to read. I figured that I would spend another night pretending that I wanted to open the book. And then there would be maybe a little drinking on the side.”
“Maybe a lot of drinking?” Denario snapped.
“Who knows?” The wizard as if anything were possible. He raised up a wavering hand. “Oh, wait, I know!”
Denario had a sense of what was coming next.
“I'll buy you a drink,” the strange fellow concluded.