Disclaimer and beta thanks in Chapter 1.

Thanks for all of your reviews! It took me a few months to put this story together, so it's nice to know that it's appreciated. You might have guessed by now that this is a Don-centered story, but the Charlie-lovers out there should be happy with the next couple of chapters.

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Chapter 3
Thursday, June 16, 2005
9:35 A.M.
Math building, CalSci

"Yo, Charlie." Don rapped on the door as he stuck his head inside his brother's office. "You busy?"

The curly-haired mathematician looked up from his desk, where he was buried behind stacks of blue books. "Kind of, yes. Is it urgent?"

Don gestured at the piles of exam books. "Grading finals?"

"Just compiling the scores. Grades are due tomorrow, and I spent Sunday golfing with Dad instead of grading." He paged through one of the books, squinted into the distance for a moment, and wrote down a number in red ink on the front. "Ouch. They are not doing well."

"Wrote a final that was too hard, did you?" Don entered the office and closed the door behind him, crossing the room to sit on a chair in front of the professor's desk.

Charlie looked at him from under his eyebrows before flipping through another blue book. "I do not write tests that are too hard. I have some students who fail to take them seriously." He punctuated his statement by circling the 65 that he had written on the cover.

"Oh, is that it," Don replied knowingly.

"It's the same test I gave last quarter, plus or minus a few questions. And I taught the class the same way. Students vary from class to class. It's just regression towards the mean." He summed another score and wrote down. Don watched as he looked at the student's name, and then broke into a grin. "Good job, Sara," Charlie murmured. "That'll get you your A."

"You keep track of everyone's grade like that?" Don wasn't sure why he was asking; Charlie could juggle dozens of pieces of information in his head at once without dropping any of them. But it made him wonder if all professors whizzed through the grading of final exams so quickly, especially those not as mathematically gifted as Professor Eppes.

"You'd be surprised how little difference the final makes in determining overall grades. Larry keeps threatening to secretly assign grades in the last week of class and just toss everyone's final in the recycling bin."

Don raised his eyebrows. "Isn't that a little unfair to the students? What if they study their butts off for the final?"

"Or what if they get their siblings to explain to them the physics that they blew off for the entire semester?" The corners of Charlie's mouth were twitching as he spoke.

"Hey, I took that final and got a B on it all by myself, thank you very much." Don glared at his younger brother. "If I'd had Larry for a professor, you're telling me I would have been stuck with a D for the class."

"Larry doesn't actually do that, it's just an observation about the likelihood of students changing their ways at the end of the term. Besides, how much do you remember about mechanics or E&M?"

"I know an object can't be in two places at one time." Don lifted the file folder he'd been holding. "Beyond that, I need your help."

"Someone's violating the basic laws of physics?"

"More like someone's tampering with evidence." He dropped the folder on top of one of the stacks of blue books. "We're trying to trace the route of a container ship that docked at Long Beach on Monday night with some contraband. We know all the places where they picked up legitimate cargo, but not where they got the illegal stuff. We've contacted ports around the Pacific Rim, but we're not having much luck. Either they have no record because their computer crashed, or the ship is recorded as being in two places on the same day, or there's some other 'coincidental' snafu."

Charlie had opened the folder and was paging through the documents: the ship's manifest, and the small bits of information they'd managed to gather from the major Asian ports in the last 36 hours. "You don't think they're coincidental."

"Well, we already know whoever's behind this has a long reach." When Charlie looked up, he went on, "They killed the informant who tipped us off. Within 12 hours of the bust."

Charlie gave a low whistle. "That's a little scary."

"Yeah, tell me about it. So what we need is to figure out the order in which the ship visited all of the ports, in order to see if there's any extra time in there where they might have slipped into another destination, and where that might be."

Charlie nodded, but didn't reply.

Then his last words registered with Don. Was that his brother's way of trying to tell him something? "Uh, you know, if you're too busy with your finals, I could come back in a couple of days."

"No, it's okay." Charlie waved at him to stay put.

"Seriously, if it's too much for you. I mean, it is pretty unnerving about Everett." At Charlie's quizzical look, he explained, "Our informant. I completely understand if you don't want to get involved."

"Don, it's not that." He shrugged and returned to his perusal of the file. "I trust that you wouldn't do anything to put me in danger."

Well, that was more confidence than Don had in himself, he thought as he stared at the top of his brother's curly head. It had become so easy so quickly to rely on Charlie and forget that he wasn't a trained FBI agent. But the sniper had reminded him of that with horrifying clarity.

He'd chewed out David but good for bringing a civilian into the line of fire. They both understood that Don wouldn't have been so furious if it was just any civilian, though it was still the younger agent's error. If Terry hadn't been called out of town for the past few weeks to consult on a case, he would have preferred that Sinclair stay out of his way. As it was, he knew that David was shaken enough by the incident that it wouldn't happen again.

And if Don had anything to say about it, Charlie would never be in the line of fire again. Which meant it was a dumb idea for him to have come here. "Maybe you shouldn't be consulting on this one until we have a better idea who we're dealing with."

Charlie was shaking his head. "You don't have to worry about that."

"Yes, I do, Charlie. You just told me you trust me to keep you out of danger, and I – "

He raised a hand to cut him off. "Don, you don't have to worry about it because I can't help you. I can't do what you're asking. I'm sorry." He closed the folder and laid it down on top of the exam books.

"What do you mean, you can't do it?" Don didn't understand what he was hearing. His brother could always do the math.

Charlie sighed. "What you're asking me to do is a variation of the traveling salesman problem."

"The what?"

As Charlie rose to his feet and crossed the room to the chalkboard, Don wondered if he was capable of explaining anything mathematical without a marker or a piece of chalk in his hand. "Say a salesman leaves home, and he has to visit a certain number of cities on his trip." He drew five large dots on the board. "There's a certain travel cost between each pair of cities." He chose one dot and drew lines from it to each of the other four, writing in a number on each of the lines between 0 and 10. Then he repeated the process for each dot, creating an intricate web of lines and numbers spanning the chalkboard. "The goal of the salesman, of course, is to visit each city while minimizing his total travel cost. And there's a certain order in which he has to visit the cities to make that happen."

Don stared at the diagram for a moment. "But the cities that are closest to each other aren't always the cheapest to travel between, because a pair that aren't adjacent might be connected by a freeway or a direct flight or something."

"That's right. That's what these weights indicate." Charlie pointed at the numbers he had assigned to each line. "For your container ship, the weights might include the time it takes to clear customs, or how long it has to wait for a berth to open up at a port. Even if the ports are all in a straight line up and down the coast, a linear order doesn't necessarily make the most sense."

He almost understood what his brother was trying to teach him, but there was still something missing. "But we're not interested in how much it cost the 'Buir Lake' to get from China or Singapore or wherever to Long Beach, just where it stopped along the way."

"But 'cost' can mean many things, not all of them monetary. These numbers -- " he tapped the board -- "can mean time as well as money. In this case, we know the total travel time, based on when the ship last left Los Angeles and when it arrived at Long Beach. Based on the cost in travel time between those ports, there should be a unique solution to the traveling salesman problem that would tell us in what order it visited the ports. Unfortunately, I can't come up with that solution."

Don frowned. "It seems like it would be easy. I mean, if I can understand the problem, it can't be too complicated, right?"

Charlie gave him a rueful grin. "Neither is Fermat's Last Theorem, and that took over three hundred years to prove. For only a few cities, it's fairly trivial to solve, but the number of possibilities goes up at a frighteningly rapid rate as you add more locations."

"Yeah, but there's fewer than forty places the ship could have gone. Can't you, what do you call it, use brute force?" It always sounded strange when Charlie used the terminology of physical violence to talk about calculating numbers. But then, he supposed that to a mathematician, that's what running a bunch of numbers without any kind of elegant equation was: a form of violence.

Charlie grimaced. "Not exactly. Say there were only twenty ports to consider. The number of possible combinations is…" He snatched up the chalk and started writing on the board. "Assuming your starting point is fixed, it's n-1 factorial. Normally, I'd divide it by two, but the travel cost might not be the same in each direction, so it's asymmetric."

He thought about it for a moment as Charlie scribbled. "Because the time it takes to go from, say, Shanghai to Seoul might take longer than Seoul to Shanghai, if there's a longer customs line at Seoul or something."

His brother shot him a grin. "That's good, Don. You're picking this up faster than a lot of my students would."

"I'm twice as old as your students," he huffed. "I have a little more experience at figuring things out. And don't you say anything." He pointed his finger at Charlie as he saw the mathematician's mouth open with what was no doubt a rude comment about his age.

Charlie spread his hands wide and gave Don an innocent look before returning to the board. "As I was saying, n-1 factorial. That's nineteen times eighteen times seventeen, all the way down." He thought for a moment, scribbled a few numbers off to the side, and then wrote 60,822,550,200,000,000 on the board.

Don shook his head. No matter how many times he saw that internal calculator of his brother's in action, it still amazed him. So did the number he had written. "That's how many possible routings there are? That's huge!"

"On a supercomputer that could check a million routes per second, that would take, um, 77,000 years. And that's only twenty cities, not forty."

"Crap."

Charlie gave a simple nod in response.

"Isn't there some kind of equation you can come up with, some kind of shortcut?"

"I knew you were going to ask that." He shook his head regretfully. "No, I can't. And you know why?"

Don raised his eyebrows in query.

Charlie tossed the chalk onto the rail. "This is P vs. NP, Don. The traveling salesman problem is a classic example of an NP-hard problem. I can't solve it – because no one can. I can run some branch-and-bound algorithms and try to at least narrow down the possibilities for you, but I'm afraid that's it."

Don rubbed a hand over his face. "I suppose I know better than to ask you to come up with a mathematical breakthrough in the next couple of days or so."

He gave a hollow laugh. "If I didn't figure it out in the three months I spent hiding in the garage, I'm not going to figure it out now."

Don looked up at his brother's rare acknowledgment of the time he'd spent avoiding their mother's deathbed. He wanted to ask him about it, like he had so many times since those terrible days when the entire family was slowly coming unwound. What had led Charlie to hide, as he put it, to focus on an unsolvable math problem instead of the unsolvable problem of Margaret Eppes' cancer? Mom had claimed to understand what was going on in her younger son's head, but she was never able to explain it to Don's satisfaction. And the fact that Charlie had brought it up, if obliquely, was an opportunity that rarely came along.

But their recent camaraderie and understanding was still a little too new, a little too tenuous, to risk by probing old wounds. And he needed whatever help his brother could give him here, even if it wasn't as neat and clean an answer as he would like. So he quirked up the corner of his mouth to acknowledge what Charlie had said, but also to indicate that he was going to let it pass. A flicker of understanding passed over Charlie's face, and then it was back to the case, and back to the math.

"Like I said, Don, I can narrow down the possibilities, but that will still take a couple of days. How urgent is this?"

"Get your grades done first." Don sighed. "We'll have to think of something else."

"Don, I'm really sorry." Charlie stared at the board. "Maybe if I tried a different approach…"

"Oh, no you don't." Don stood up and walked over, prepared to forcibly pull his brother away from the chalkboard if he had to. "There's no lives at stake, nothing that can't wait a few days. You don't have to do this, Charlie. We'll find another way."

He gave the board an almost longing look before turning away. "You're right. I have other things to do, and you have other approaches you can take. Right?"

"That's right." Don watched as his brother crossed back to his desk and plopped down behind the piles of exams. "Hey, I'll see you for dinner tomorrow night, okay?"

"You don't have to check up on me, Don. I'm not going to start working on P vs. NP." Charlie's tone was slightly exasperated as he rifled through another blue book.

"I know. I just feel like ribeye."

Now there was a grin on Charlie's face, though he remained focused on his work. "Someday you're going to have to tell me how you do that."

The corners of Don's eyes crinkled as he smiled. "Just something they taught us at Quantico, little brother."

His response was a dismissive wave. "Yeah, yeah. See you tomorrow."