“I’ve been thinking about going vegetarian,” Hassan told her, his arm draped around her waist.

“Well just don’t get skinny,” Katrina answered, and then they kissed right in front of Colin, who still couldn’t get his head around any of this.

“All right, boys,” Mr. Lyford said, smacking Colin on the back rather too hard. “Ready for yer first hunt?”

Colin nodded with some reluctance, waved good-bye to Lindsey and the others, and headed out with Hassan, whose orange vest was not quite big enough to fit comfortably around his chest. They set off down the hill, not following a trail, just bushwacking. “We begin by looking for rootings ,” Mr. Lyford explained. “Places where a hog has been turning up the soil with his long snout.” He talked to them like they were nine years old, and Colin was wondering if Mr. Lyford thought they were younger than they actually were when Mr. Lyford turned back to them with a can of chewing tobacco and offered them each a pinch. Colin and Hassan both politely declined.

Over the next hour, they hardly spoke, because “the feral hog may shy away from the human voice,” Mr. Lyford said, as if the feral hog did not shy away from other voices, such as those of Martians. Instead they walked slowly through the woods, their eyes scanning the ground in search of rootings, their guns pointed down into the dirt, with one hand on the stock and the other sweating against the barrel. And then, finally, Hassan saw something.

“Uh, Mr. Lyford,” Hassan whispered. He pointed to a patch of dirt that had been dug out haphazardly. Mr. Lyford knelt down and inspected it closely. He sniffed at the air. He dug his fingers into the dirt. “This,” Mr. Lyford whispered, “is a rooting. And you, HASS-in, have found a fresh one. Yes, a hog has been here recently. Now, we track it.”

Mr. Lyford doubled the pace then, and Hassan struggled to keep up. Mr. Lyford found another rooting, and then another, and he felt sure he had the trail, so he took off in a kind of race-walk, his arms pumping so that the gun wiggled in the air like he was in color guard. After about five minutes of that, Hassan hussled up to Colin and said, “Please God, no more run-walking,” and Colin said, “Seriously,” and then they both together said, “Mr. Lyford?”

He turned around and walked several paces back to the boys. “What is it, boys? We’re on the trail here. We’ve got a hog almost in sight, I can feel it.”

“Can we slow down?” Hassan asked. “Or take a break? Or take a break and then slow down?”

Mr. Lyford sighed. “Boys, if you are not serious about hunting the feral pig, then I can just leave you here. We’re on the trail of a hog,” he whispered urgently. “This is no time for lollygaggin’ or dillydallyin’.”

“Well,” suggested Colin, “maybe you should just leave us behind then. We can sort of protect your flank, in case the feral pig doubles back around.”

Mr. Lyford looked extremely disappointed. He pursed his lips and shook his head sadly, as if he pitied the poor souls who were unwilling to push their bodies to the limit in search of the feral pig. “Very well, boys. I’ll come back and get ya. And when I do, it’ll be to get your help carryin’ out a gorgeous hog.” He started to walk off and then stopped and pulled out his can of chewing tobacco. “Here,” he whispered, handing it to Colin. “I fear the hog will smell the wintergreen.”

“Uh, thanks,” said Colin, and Mr. Lyford ran off into the distance, weaving through the forest in search of more, fresher rootings.

“Well,” Hassan said, squatting down to sit on a rotting fallen tree. “That was fun. Jesus, I didn’t think hunting involved so much walking. We should have gotten the sweet gig Lindsey has, sitting in a tree and making out and waiting for a pig to walk by.”

“Yeah,” said Colin, absentmindedly.

“Hey, d’you bring the minirecorder?” asked Hassan.

“Yeah, why?”

“Gimme,” he said. Colin pulled it out of his pocket and handed it over.

Hassan pressed record, and then started up with his best Star Trek voice. “Captain’s log. Stardate 9326.5. Hog hunting is incredibly boring. I think I’ll take a nap and trust in my brilliant Vulcan companion to let me know if any extremely dangerous feral hogs walk by.” Hassan handed back the minirecorder and scooted over to lie down beside the fallen tree. Colin watched Hassan close his eyes. “Now this,” Hassan said, “is huntin’.”

Colin sat there for a while listening to the wind tease the trees as clouds moved in above them, and he let his mind wander. It went to a predictable place, and he missed her. She was at camp still, and they didn’t let her use a cell phone, at least not last year, but just to be sure he pulled his phone out of his camouflage pants pocket. He got reception, amazingly, but had no missed calls. He thought of calling but decided against it.

He would call when he completed the Theorem, which led him back to it and the seemingly intractable III Anomaly. Eighteen out of nineteen Katherines worked, but this utterly insignificant blip on the Katherinadar came out looking like a jacked-up smiley face every time. He remembered her again, thought back to whether he’d failed to account for some facet of her personality in his calculations. Admittedly, he’d only known her for twelve days, but the whole idea of the Theorem was that you didn’t have to know someone intimately in order for it to work. Katherine III. Katherine III. Who would have thought that she, among the least important to him, would prove the Theorem’s downfall?

Colin spent the next ninety minutes thinking, without ceasing, about a girl he’d known for less than two weeks. But eventually, even he grew tired. To pass the time, he anagrammed her sprawling name: Katherine Mutsensberger. He’d never anagrammed her before, and he was fascinated to find the word “eighteen” within her. “Me returns eighteen barks; eighteen errs makes burnt.” His favorite: “Remark eighteen, snub rest.” But that didn’t really make sense, because Colin had certainly remarked all nineteen.

Hassan sniffled and his eyes shot open and he looked around. “Fug, are we still hunting? Big Daddy needs some lunch.” Hassan stood up, reached into the cargo pockets of his pants, and pulled out two badly smushed sandwiches in Ziploc bags. “Sorry, dude. I fell asleep on lunch.” Colin opened the canteen hooked to his belt buckle, and they sat down for turkey sandwiches and water. “How long did I sleep?”

“Almost two hours,” Colin said between bites.

“What the fug d’you do?”

“I should have brought a book. I just tried to finish the Theorem. The only problem left is Katherine III.”

“Oo vat?” Hassan asked, his mouth full of a too-mayonnaisy sandwich.

“Summer after fourth grade. From Chicago, but she was homeschooled. Katherine Mutsensberger. One brother. Lived in Lincoln Square on Leavitt just south of Lawrence, but I never visited her there because she dumped me on the third-to-last day of smart kid camp in Michigan. She had dirty blond hair that was a little curly and she bit her nails and her favorite song when she was ten was ‘Stuck with You’ by Huey Lewis and the News and her mother was a curator at the Museum of Contemporary Art and when she grew up she wanted to be a veterinarian.”

“How long d’you know her?” asked Hassan. His sandwich was finished, and he wiped the remnants of it on his pants.

“Twelve days.”

“Huh. You know what’s funny? I knew that girl.”

“What?”

“Yeah. Mutsensberger. We went to all these lame-o homeschooling events together. Like, bring your homeschooled kid to the park so she learns how to be less nerdy. And, take your homeschooled kid for a homeschool picnic so the Muslim kid can get his ass kicked by all the evangelical Christians.”

“Wait, you know her?”

“Well, I mean, we don’t keep in touch or anything. But yeah. I could pick her out of a lineup.”

“Well, was she quite introverted and a little dorky and she’d had one boyfriend when she was seven who dumped her?”

“Yup,” said Hassan. “Well, I don’t know about the boyfriend. She had a brother. He was a first-rate nutcase, actually. He was into spelling bees. Went to Nationals, I think.”

“Weird. Well, the formula doesn’t work for her.”

“Maybe you’re forgetting something. There can’t be that many goddamned Mutsensbergers in Chicago. Why don’t you call her and ask?” And the answer to that question—“because it literally has never occurred to me”—was so outrageously dumb that Colin just picked up the phone without another word and dialed 773.555.1212.

“What city?”

“Chicago,” he said.

“What listing?”

“Mutsensberger. MUTSENSBERGER.”

“Hold.”

The computer voice recited the number, and Colin pressed 1 to be connected immediately free of charge, and on the third ring, a girl picked up.

“Hello,” she said.

“Hi. This is Colin Singleton. Is—is, uh, Katherine there?”

“Speaking. What did you say your name was?”

“Colin Singleton.”

“That’s so familiar,” she said. “Do I know you?”

“When you were in fourth grade, I may have been your boyfriend for about two weeks at a summer program for gifted children.”

“Colin Singleton! Oh yeah! Wow. Of all people . . .”

“Um, this is going to sound weird, but on a scale of one to five, how popular were you in fourth grade?”

“Uh, what?” she asked.

“And also do you have a brother who was into spelling bees?”

“Um, yeah, I do. Who is this?” she asked, suddenly sounding upset.

“This is Colin Singleton, I swear. I know it sounds weird.”

“I was, I don’t know. I mean, I had a few friends. We were kinda nerdy, I guess.”

“Okay. Thanks, Katherine.”

“Are you, like, writing a book?”

“No, I’m writing a mathematical formula that predicts which of two people will end a romantic relationship and when,” he said.

“Um,” she answered. “Where are you, anyway? Whatever happened to you?”

“What happened, indeed,” he answered, and hung up.

“Well,” said Hassan. “Boy. She must think that you’re STARK RAVING BONKERS!”

But Colin was lost in thought. If Katherine III was who she claimed to be, and whom he remembered her to be, then what if. What if the formula—was right? He called her again.

“Katherine Mutsensberger,” he said.

“Yes?”

“It’s Colin Singleton again.”

“Oh. Um, hi.”

“This is the last question I’ll ever ask you that sounds completely crazy, but did I by chance break up with you?”

“Um, uh-huh.”

“I did?”

“Yeah. We were at a campfire sing-along and you came over to me in front of all my friends and said you’d never done this before, but you had to break up with me because you just didn’t think it was going to work long-term. That’s what you said. Long-term. God, I was devastated, too. I thought you hung the moon.”

“I’m really sorry. I’m sorry I broke up with you,” Colin said.

She laughed. “Well, we were ten. I’ve dealt with it.”

“Yeah, but still. I’m sorry if I hurt your feelings.”

“Well, thank you, Colin Singleton.”

“No problem.”

“Is there anything else?” she asked.

“I think that’s it.”

“Okay, well, you take care of yourself,” she said, the way you might say it to a schizophrenic homeless person to whom you’ve just given a dollar.

“You too, Katherine Mutsensberger.”

Hassan stared at Colin unblinkingly. “Well, dress me up in a tutu, put me on a unicycle, and call me Caroline the Dancing Bear. You’re a fugging Dumper.”

Colin leaned back against the rotten tree, his back arching over it until he was staring at the cloudy sky. Betrayed by his vaunted memory! He had, indeed, remarked eighteen and snubbed the rest. How could he remember everything about her and not remember that he dumped her? And for that matter, what kind of asshole was he to have dumped a perfectly nice girl like Katherine Mutsensberger? “I feel like I’ve only ever been two things,” he said softly. “I’m a child prodigy, and I’m dumped by Katherines. But now I’m—”

“Neither,” Hassan said. “And be grateful. You’re a Dumper and I’m making out with a ridiculously hot girl. The whole world is turned upside down. I love it. It’s like we’re in a snow globe and God decided he wanted to see a blizzard so he shook us all the fug up.”

Just as almost no true sentence beginning with I could be spoken by Lindsey, Colin was watching all the things he’d thought were true about himself, all his I sentences, fall away. Suddenly, there was not just one missing piece, but thousands of them.

Colin had to figure out what had gone wrong inside his brain, and fix it. He returned to the central question: how could he have completely forgotten dumping her? Or, almost completely, because Colin had experienced a dim flash of recognition when Katherine told him the story of his dumping her in front of her friends, a feeling vaguely like when a word is on the tip of your tongue and then someone says it.

Above him, the interweaving branches seemed to split the sky into a million little pieces. He felt like he had vertigo. The one facility he’d always trusted—memory—was a fraud. And he might have gone on thinking about it for hours, or at least until Mr. Lyford returned, except at that very moment he heard a weird grunting noise and simultaneously felt Hassan’s hand tap his knee.