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Amber pulled the paper out, feeling a thrill of excitement as she saw what it was.
"Here!" she said, holding it up for Simon to see. There was a hand-drawn version of the Konigsberg bridge problem on it, along with a message in small, neat handwriting.
"This is a demand that Victoria walk over all the bridges of Verdice by midnight or face a punishment for failing it," Amber said. Excitement flooded her as she realized what this meant. "Does the coroner have a time of death for Victoria Crossing yet?"
She saw Simon check something on his phone.
"A little after midnight."
"Because she didn't do what he wanted." Amber could see it all now, could finally see how these murders worked. "He's using the Konigsberg bridge problem as some kind of twisted test. He's forcing his victims to solve it or die."
Simon looked at her, his expression grim. "That's insane."
"I know," Amber said, her mind racing. "But it's the only thing that makes sense." And there was one part that made it even more awful. "But Simon, this is worse than you think."
Simon didn't look happy about that. "Worse than a killer who murders people because they can't solve a puzzle he sets? That sounds pretty bad anyway, Amber."
Amber nodded. "This is definitely worse than that. This is all based on a famous mathematical problem: the Konigsberg bridge problem. It's very old. The mathematician Euler solved it in the 18th century."
Simon frowned at that, clearly not understanding yet. "That doesn't sound so bad, Amber. A math problem that has been solved... shouldn't the victimsknowthe answer? Victoria Crossing, in particular, if she taught math?"
"I think she did," Amber said. "I think that's why we found her here rather than out on one of the city's bridges. Euler proved that the Konigsberg bridge problem is only possible to complete with an even number of bridges, so either adding one or taking one away from Konigsberg's original seven."
"The same as Verdice," Simon said. Amber could see from the gravity of his expression that he understood. "He sets them an impossible problem, forces them to play his game, and then kills them when they realize that they can't solve the puzzle he's forced them to try to complete."
"Exactly," Amber said. "This isn't someone playing a sick game with his victims. That would be bad enough but this… it's just a way of tormenting them. And if they refuse to play..." she gestured back towards the main room of the apartment. "Victoria was a math TA; she would have known about the problem. She would have known that the problem was impossible to solve. Maybe she thought it was a joke, or maybe she was planning to take it to the cops in the morning, but either way, she didn't want to play the killer’s game. She probably thought that she was safe enough in here, well away from the bridges."
"So he broke in here and killed her for it," Simon said. Now, as he started to understand the full cruelty of what had happened, Amber could hear an echo of the horror that she felt in his voice.
Amber choked back a sudden burst of anger that threatened to rise up through her at the thought of what the killer had done. She was a puzzler at heart. She loved solving tough problems and setting them. Occasionally, in her former job as a puzzle editor, she'd really let herself go, let herself make problems that would have challenged someone on her level of puzzling skill, rather than trying to judge what the readers could and couldn't handle.
Those problems had verged on the impossible, but they hadn'tbeenimpossible. That wouldn't have been fair; that wouldn't have been right. A puzzle that didn't have a real solution wasn't truly a puzzle; it was just a way to inflict suffering on people. To Amber, a puzzle without a solution felt simply… wrong.
Amber thought about Mia and Kelly. They'd both been on bridges, which meant that they'd both tried to solve the problem. They’d both set out, trying to finish it. Maybe they hadn't known that it was impossible, maybe they’d hoped that there was a difference in the layout of the city that would allow it to work here, or maybe they'd been so scared that they'd tried it anyway. They'd gone out with the hope that they might survive, and the killer had followed, knowing that they were dead from the start.
What kind of mind could do that to someone?
CHAPTER NINETEEN
He moved with the utmost caution as he approached the house, but then, he was always careful. He never took risks that he didn’t need to when it came to this. He watched, and he waited; he calculated every move that he was going to make, and he acted only when he knew that the probability of success was approaching one hundred percent.
Mathematics was fundamental to the ordering of the universe, governing it and setting out the limits within which anything was possible. He knew this better than anyone, and he reveled in it. There was something magical about the way that numbers could be used to shape the world, predict outcomes, and control variables. It was a power that he wielded with great skill and precision. No, not magical, because magic was irrational. It broke the rules. This was pure rationality, real understanding. Itwasthe rules of everything.
As he approached the house, he felt a thrill of excitement. This was his game, and he was winning it from the start.
Not that the game worked the way the women he killed thought that it did. They were stupid. They didn't understand. Well, of course, they were. The first two had been so foolish that they actually tried to solve an impossible puzzle. Victoria thought that she was clever by refusing to take part, but that was just a different kind of move in a greater game. Another wrong choice, another proof that she was lesser, as clean as any mathematical proof could be.
He'd learned a lot about games and problems over the years. Math loved to examine that kind of thing, loved to look at every facet of human behavior and ask what the optimal approach was.
Not that it had helped with his first interactions with these women. He'd calculated exactly what he needed to do and say, worked out the probabilities precisely, but it still hadn't helped. Mia had shot down his invitation to dinner with a laugh, as if it were a stupid idea as if he weren't brilliant, exceptional. Kelly had whispered about him behind his back, saying that he was losing it. Victoria... well, she'd done something far, far worse. She'd dared to correct some of his work. As ifhe'dbeen the one to do something wrong.
He couldn't have been. He didn't do things wrong. Not when it came to math. He didn’t make those kinds of mistakes. It had beenherfault, not his.
Like most women, they all thought that they were so perfect, so clever. They didn't see that they were just... less than him. They didn't understand that he was smarter than they could ever be, that he understood the world on a level that they could never dream of touching.
They should have been grateful for his attention. Instead, they’d treated him like he wasn’t brilliant.
They had to be shown that they weren't as smart as they thought, that they were stupid, weak, and worse. It wasn't enough for them to die; they had to die knowing that they'd lost and that they'd been helpless from the moment he'd decided that they should die. They had to die, knowing that there had never been a chance for them to survive.
