The Fibonacci Murders

by Dale E. Lehman

  A chill ran down Montufar’s spine. She laid her head on her desk and folded her hands over it as if curling into a defensive posture, or hiding from the world.

  She knew what it was.

  God in heaven, she knew what it was.

  ∑

  By the time Peller and Dumas arrived, headquarters was a hive of activity. In addition to the usual cases, six crank calls claiming responsibility for the previous day’s killings had come in, while eight letters from would-be mad golfers and serial killers had been delivered. Captain Morris had intended to release Julian Szwiec’s name and particulars and ask the public for information on his whereabouts, but the Mason killings had preempted everything, so now she was in overdrive, attempting to gather information for the rescheduled press conference to cover both Szwiec and the hunt for Leo. The fact that Szwiec was implicated in the Mason killings was, from her view, a strong positive development. The fact that he’d slipped through their fingers the day before, however, was going to make things very ugly.

  Tom Kaneko had returned to his borrowed cubicle and was busy reviewing the latest information, his concentration so intense he didn’t notice the bedlam surrounding him.

  And then there was Montufar, looking pale and exhausted as she hooked both Peller and Dumas by the arm and steered them towards an empty conference room. “We have to talk,” she said.

  “How’s your brother?” they asked simultaneously.

  “He’ll live,” she replied. “We have a bigger problem.”

  She pushed them into the conference room and was about the close the door when a voice cried from across the room, “Phone call, Lieutenant.” Peller craned his neck to look around Montufar. A new detective whose name he couldn’t recall pointed emphatically at the receiver he was holding aloft and mouthed what looked like, “It’s him.”

  “Transfer it in here,” Peller called back. When the phone rang he pushed the speaker button. “Peller,” he spat.

  “Hello again, my friend,” Leo’s thin voice murmured.

  “I’m not your friend,” the detective growled.

  A rattling laugh sounded on the other end. “But I will do you a favor anyway. Some new information. Write this down.”

  Dumas pulled a pen and notepad from his pocket and nodded.

  “Go ahead,” Peller said.

  “I start with two.”

  They all stared at the phone, even Dumas, who wrote nothing.

  “What?” Peller demanded.

  “I start with two,” Leo repeated. There was a click and the line went dead.

  Dumas looked confused. “Didn’t we already start with zero?” he asked, but scribbled down the message anyway.

  Montufar pulled out a chair and collapsed into it, shutting her eyes.

  Peller dialed an extension and told the person on the other end, “Have Tom join us in the conference room, please.” Sinking into a chair next to Montufar, he asked her, “What did you want to talk to us about?” The calmness in his voice amazed even himself.

  She opened her eyes. “I think he’s a soldier. Or used to be one.”

  Dumas nodded. “I can see that. Or possibly a cop gone bad. That would account for the haircut. And it’s clear he knows his way around firearms. A Luger? That’s not your average gun.”

  “It’s more than that,” Montufar continued. “It’s the way each killing has been planned and executed. A couple of sniper attacks, a couple of executions. One like an encounter in a narrow street, except it was a service corridor in the mall, and even one—Lorna Bigelow—that might be like a covert assassination. I think this guy was in Iraq or Afghanistan and brought the war home with him.”

  Peller let the idea chase its tail around his brain until Dumas interrupted: “Problem.”

  They waited while he formulated his thoughts. “Look at it this way,” he began, but got no further as Kaneko abruptly opened the door.

  “You wanted to see me?” the mathematician asked.

  Peller motioned him to a chair. “Leo called again.”

  Kaneko sat. “I thought he said eight was the last number?” Dumas shoved the notepad to him, and he gazed at it without expression.

  “What do you think?” Peller asked.

  “I think we are in trouble. What do you think?”

  Peller sighed heavily. “He’s starting a new sequence.”

  Dumas added, “It starts the same way as the first sequence. ‘I start with…’ The numbers in the new sequence will have the same meanings as the ones in the first sequence.”

  Kaneko nodded, “Likely so. But we will need at least three numbers before we have a chance of determining what this new sequence is.”

  “I’d think,” Peller said, “it would be obvious. If it follows the Fibonacci pattern, it would be two, three, five, eight, thirteen, twenty-one, and thirty-four.”

  There was a moment of silence that seemed to drag on and on. Then Kaneko stood and began to walk slowly around the table, hands clasped behind his back. “What troubles me in this particular situation,” he began, “is that the Fibonacci sequence, which you are familiar with, is merely a special case of something called a Lucas sequence, which you most likely do not know. Technically, a complementary pair of Lucas sequences generate the Fibonacci sequence. A Lucas sequence is specified by a recurrence relation and a pair of fixed integers. So there are an infinite number of such sequences and thus an infinite number of complementary pairs of such sequences. And Lucas sequences are merely one type of sequence. It is impossible to know what sequence one is dealing with if all one has is a single number. Indeed, it is impossible to know based on two consecutive numbers.”

  “Clear as mud,” Dumas said with the petulant air of one whose academic strengths did not include mathematics.

  “Um, okay,” Montufar said, taking up the slack. “You’re right, none of us know about Lucas sequences. We didn’t know about Fibonacci until this all started. But what does it mean, that he’s using a Lucas sequence? I know what an integer is, but what makes them fixed? What’s a recurrence relation? How can we use it to help predict the next murder, and how likely is it that Leo knows it?”

  Kaneko stopped pacing and gazed at his shoes. “Not likely,” he admitted. “Yet I suggest that we reserve judgment.”

  “Point taken,” Peller said. “Thank you.”

  Kaneko bowed slightly and withdrew.

  “So what we’re looking at,” said Dumas to Peller, “is a psychopathic soldier who was a mathematician in a past life and who just happens to know you even though you don’t know him? Are we actually getting anywhere with this?” He took back his notepad and studied what he’d written. “What if… “ he mused, “what if…despite higher mathematics…Leo isn’t just a psycho? What if he doesn’t think he’s still fighting the war? What if he thinks he’s fighting a war, though, and he’s told us more or less how he’s going to fight it? Up to now he’s been saying, ‘This is what I’m going to do.’ But now—” he pushed the notepad to Peller—“now he’s saying, ‘I’m going to start doing it.’ He either wants us to stop him before he does it, or he wants the world to know that he’s the one doing it.”

  None of them had noticed that Captain Morris had quietly opened the door and was listening until she rapped on the wall. “Sorry to interrupt,” she said, “but I want the three of you with me at the press conference to answer any questions I can’t answer. And I want us to agree on one thing before we get there. Job one is nabbing Julian Szwiec. All speculation aside, if he was at the Mason home, then he can lead us to his partner and that’s the end of it.”

  Peller didn’t think it would be that easy, but it wasn’t the time to argue. Without a word, he nodded assent, and the three of them rose to follow their boss.

  ∑

  Every TV station and newspaper in the Mid-Atlantic region plus CNN and the BBC seemed to have
jammed journalists into the lobby of Northern District Headquarters, where Captain Morris had instructed a lectern and a small table and several chairs to be placed for the press conference. The cacophony, she thought, could drown out the most over-amped rock concert ever played at Merriweather Post Pavilion. Yet when she came into the gathering followed by Peller, Montufar, and Dumas, a sudden silence descended. The detectives took seats at the table while she marched straight to the lectern and began quickly, so as not to allow anyone else time to get in a word.

  “Good morning. For those of you who don’t know, I’m Captain Whitney Morris, head of the Howard County Police Criminal Investigations Division. With me are Detective Lieutenant Rick Peller, Detective Sergeant Corina Montufar, and Detective Sergeant Eric Dumas. We’re here today with updates on the so-called golfer muggings and the series of murders that have taken place in Howard County over the past week. I know you’re anxious to get to the latter, but first I want to give you some information about the muggings.”

  Some muttering erupted in the crowd, but Morris paid it no heed. “Previously we released a sketch of a suspect. Thanks to information provided by a witness who saw that sketch on the news, we have been able to identify the suspect as Julian Szwiec, age twenty-two, currently unemployed. Mr. Szwiec is armed and dangerous. During a pursuit he shot and wounded two officers who discovered him at his home near Centennial Park in Columbia. Anyone having any information about Mr. Szwiec’s whereabouts should immediately contact our department. Do not attempt to approach or apprehend him yourself. Again, he is armed and extremely dangerous.”

  She paused for a look around the room. So far she sensed she was delivering what they wanted to hear, but that wasn’t going to last long. “There is one more thing,” she told them. “As you know, not one but two terrible tragedies occurred yesterday: the brutal murders of an entire family in Clarksville, and the murder of state senator Roger Harrison. Both of these murders appear to be related to the killings committed over the past week. But the murders of the Mason family, as tragic as they were, may have given us the means to put a stop to these horrible acts and bring the guilty parties to justice. We have strong evidence that Julian Szwiec was present in the Mason home that morning along with another man.”

  Pandemonium erupted. Every reporter in the room shouted out questions and gestured wildly in a frantic bid for attention. Morris called for quiet several times but could barely hear herself over the din. Finally, she stepped back from the microphone and put her hands on her hips, directing a motherly scowl at the throng. Oddly enough, the noise gradually died down. She stepped forward and continued.

  “I know you all have questions,” she told them, “and we’re here to answer them as best we can. But first let me give you the details as we know them.”

  For the next five minutes Morris laid out the basic information on the shooting of Roger Harrison, including the description of the killer as given to Peller by Virginia Smullyan, and a somewhat less detailed account of the Mason family murders. She left out the news that a gun had been located and said only that an eyewitness had put Szwiec at the scene at about the time of the killings. She did call the killings “execution-style,” which prompted another outburst of raised hands and questions.

  The first question Morris took was the one she had been dreading. The Baltimore Sun reporter asked trenchantly, “So your officers let Julian Szwiec escape, after which he killed the Masons?”

  “Mr. Szwiec was armed and fled into the woods of Centennial Park when the two officers tried to apprehend him. He shot them in the ensuing chase, after which they were unable to continue the pursuit. We do not know yet whether he killed the Masons. We do know that he was there and that he played some role in the crime, but there was one other person with him, who might be the real killer. Either way, we view the apprehension of Mr. Szwiec as instrumental in ending this killing spree.”

  Morris signaled the CNN reporter, a pixieish redhead with a scattering of freckles across her nose. “Do you have any evidence that Szwiec was involved in the other killings?”

  “Not at this time,” Morris replied.

  Before the Captain could call on someone else, the reporter fired off another question. “So was he at the Mason home or in the Mason home? And if he was in the Mason home, how would you know that?”

  “I’ll let Detective Dumas answer that question.” Morris cast a sidelong glance at her colleague.

  Dumas pulled the table microphone over. “He was in the house. We have a witness who places him there at the time of the murders.”

  Morris gave him a small, quick smile. Nice deflection, she thought.

  Except the reporter wasn’t deflected. “So there was someone in the house who wasn’t killed?”

  Dumas assumed a poker face. “There are many ways a witness might place someone inside a house at a particular time, ma’am. With the killer still at large, we don’t want to reveal too much about that so as not to endanger the witness.”

  Morris almost laughed. The man had a definite theatrical streak. She signaled the NPR reporter.

  “You said previously that these killings are related to Fibonacci numbers. Do yesterday’s murders follow that pattern and can you elaborate on what exactly it is?”

  “They do follow that pattern,” Morris said. “But that’s all I can say at this moment.”

  “Well, if the murders are each linked to successive numbers in the sequence,” the journalist pointed out, “anyone can see that the next few numbers are very large. Are we talking about body counts? Are we looking at something like a terrorist attack?”

  Before Morris could reply, Peller took the microphone. “These are not terrorist attacks,” he said sharply. “People are right to be concerned, but we have no immediate reason to fear another 9/11. The numbers are related to the murders in a complicated way that we are not at liberty to discuss.”

  Morris next selected a cub reporter for the local newspaper, The Columbia Flier. He had a somewhat timid look about him, as though he wasn’t sure he should be speaking at all. She hoped that meant his question would be easy.

  “I wanted to ask Sergeant Montufar—” he began, and the detectives exchanged surprised glances—“how is your brother doing?”

  Montufar didn’t know the young man from Adam, and the question crept up her spine. Hesitantly, she took the microphone. “He’s doing okay,” she said. “Why do you ask?”

  “Well…” The reporter glanced around at his colleagues a bit sheepishly. “I sort of know your sister Ella. She mentioned the accident but didn’t have time to go into details.”

  Montufar took a relieved breath and smiled at him. “I don’t think she’s mentioned you before.” That got a general laugh, and the young man’s face flushed scarlet. “But thank you. He’s doing fine.”

  Chapter 11

  It had occurred to me, if not to the police, that in the age of the Internet it was not necessary to be highly trained in mathematics to make use of relatively complex mathematical concepts. I don’t mean that just anyone might learn to calculate third order differential equations by reading a website, but most any reasonably intelligent person could, with sufficient effort, teach themselves how to calculate various forms of sequences.

  This led me to a conclusion I did not at once share with Rick Peller. That failure to consult was a mistake. ∑

  Until the new sequence began to take shape, Tomio Kaneko didn’t see much he could do to help the detectives, and in any case he had classes to teach on Tuesday afternoon. So he left headquarters shortly before noon and returned to his home in the well-heeled Baltimore neighborhood just north of the Johns Hopkins University campus. His house, set amid early twentieth-century homes—some of which bordered on mansions—was one of the more modest in the area. Kaneko disliked pretense and ostentation, but he and his wife Sarah had raised six children, so living space was a necessity. And now that the
y had three grandchildren, with one more on the way, he couldn’t see downsizing.

  He pulled into the left bay of his three-car garage and pushed the button on the remote to close the door. Once inside he made his way to the kitchen, where he found Sarah heating up a pot of soup and assembling a couple of chicken salad sandwiches. She flashed him a radiant smile. “I knew you’d be home for lunch,” she said, “so I thought I’d throw something together.”

  He put a hand on her shoulder and squeezed gently. Her smile hadn’t changed in forty years. He remembered little of the day they met except for her smile. She was a thin woman, about the same height as himself, with short, dark hair. She had Japanese ancestry like himself, but also Portuguese heritage on her mother’s side. It was hard to say whether her features should be classified as Asian or European.

  “Have you been able to help them?” she asked.

  He sat at the table and watched her work. “It is hard to know. I have studied all the material they could give me, but there is little to go on in terms of the mathematical angle of the case. I am very much afraid more people will die before I can tell them anything useful.”

  She must have detected a note of frustration or sadness in his voice, he thought, because she stopped what she was doing and turned to face him with a resolute expression. “You are not a policeman. They probably knew it was a long shot asking you to help them.”

  “Yes. Still, I wish I could do more. And perhaps I can.”

  Sarah didn’t ask. She brought the meal to the table and sat next to him. They ate in silence for a time while he mulled over whether or not to tell her what he had in mind. Sarah had always been supportive, even when his ideas were slightly harebrained. Not that he had ever been much of a maverick, although he did sometimes have his moments. But this was likely more harebrained than anything he’d previously done.