Occasional Puzzle: Where in the World is Carmen 5Chan Diego? Part 2

…continued from Part 1…

“So…what did you say brings you by?”  Jake began.

Shelby stared at him, perplexed.  “But, we just…”

“I should probably explain,” Jake interrupted.  “You’ve heard I had some issues with concussions.  My memory is…not good.”

“I’d heard that, but…you’re running a detective agency.  How can you do that without a functional memory?”

“My memory isn’t completely shot, it’s just…selective.  Some things I can remember just fine.  Other things won’t stick at all.  Most things, actually.”  Jake pulled a notebook out of the top drawer of his desk.  “I’m usually okay if I take notes, though.  So lay it on me.”

Shelby was held up his attache case in front of his body, as though Jake’s condition were infectious and he was trying to ward it off. “A lot of this is squiddish to me, so I’m sorry if there’s some stuff that isn’t clear,” he said, a shade of nervousness creeping into his voice. “But once all of those hammers – air traffic control, the commodities markets, the electrical grid – dropped at the same time, the everyone on the darknet all agreed that 5Chan was the only one who could have pulled it off. So the NSA started trying to sniff out where he might be. What they found…well, they didn’t find him, but they did find some of his traffic. They couldn’t read it – it was all encrypted – but they at least were able to figure out where it was coming from, and where it was going. In a sense.”

Shelby pulled a piece of paper out of the attache case. “He’s behind twenty proxies. He’s got them in different cities all over the world.”

Jake jotted all of this down. He frowned. “I don’t see why you need me for this. Just burn through the proxies and see what’s at the end of the rainbow.”

“You don’t understand, Jake. The proxies don’t lead anywhere. All the data just goes in a circle – it starts at one proxy, and then ends back up there again later. And maybe that loop means something, but somehow this loop is tipping off 5Chan to the fact that we’re sniffing at his traffic.”

“The first guy the NSA turned loose on this – who was actually had been in deep cover for years; codenamed Meatball – tried to insert a message into the loop, just to see where it would ultimately end up. Except Meatball made a mistake. He didn’t learn anything about where 5Chan was, but an hour later his entire system was filled with kiddie porn and an extremely detailed report was sent to us at the FBI. Along with a similar report being sent to six major media outlets. We had to bring him in – we had no choice – and now nobody has any idea what to do with him. Obviously he’s blown as an agent but they don’t want to compromise the entire surveillance program he was running. And of course they don’t want Meatball sent to jail; he wouldn’t last ten minutes.”

“And the second guy?”

“He’s dead. He was ‘outed’ to the very jealous husband of a woman he’d never even met. The guy laid in wait for him on his morning jog, thanks to the route that 5Chan helpfully provided by hacking his fitness tracker.”

“Sounds pretty heavy.  What makes you think I’d have any interest in mucking around with this?”

“For one thing, they approved the budget for it.”

“That helps,” Jake conceded.

“And we figured out what the guys were doing wrong. Meatball skipped a city. Barnes hit the same city twice. The lab boys are pretty sure that if we can find a path where we hit each city once – and only once – they’ll at least be able to listen in without him knowing.” Shelby pushed the list of cities across the table. “Here are the cities – each one connects to three others.”

“Ah,” Jake murmured, poring over the paper. “Twenty cities. Three connections to each. It’s a dodecahedron”

“A what?”

Jake reached into his desk.  “This is from back before my memory started to go – a fellow player hired me to authenticate a first-edition Monster Manual he bought on e-Bay.  He left this me this as a gift.”  Jake set a twelve-sided die on the table.  “It’s made out of amethyst.”

Shelby picked it up.  “It’s nice.  But this only goes up to twelve.  I thought you said twenty.”

“It’s got twenty corners.”  Jake took a blank sheet of paper and drew a series of lines on it.  “If we flatten the dodecahedron into a two-dimensional space, this is what we’ll get.  Twenty points, each of them with connections to three others.”

Jake continued.  “So the trick is to start at this point at the top, and then connect through all of the other points without hitting the same point twice.”

Shelby looked hopeful.  “So you think you can do it?  You can help us catch this maniac?”

A smug grin crept across Jake’s face.  “Oh, I’ve already done it,” he said.  “Would you like to see how?”

—

Puzzle Summary: Find a pathway through the network of proxies (starting at the blue point at the top) that passes through every other point exactly once and returns to the origin.

LINK TO PUZZLE SOLUTION