Page 229 of Claim Me
Marcel tilts his head slightly, probably testing the structure of that answer. "So you’re saying the behavior follows from aggregation?" He clears his throat.
"Yes, the complexity is emergent, not explicit," Blue says.
A short pause, then Marcel presses again, like he’s probing for a weakness.
"And you can justify that without computing it?"
Blue’s mouth curves faintly.
"You don’t need to compute it," he says. "You reframe it. Count divisor contributions as pairs instead of values. Each term corresponds to how often a number divides others. You’re effectively summing a reciprocal structure."
I feel something clear at the edges of that, enough to see the outline. Blue is correct, and Marcel looks even more lost now, like his own challenge might have gotten away from him.
"Which is why the logarithm appears," Blue continues. "You’re integrating over density, not stepping through values."
Marcel is still for a moment, and I can almost see his brain overheating as he measures whether the argument holds. It does, by my judgment, but I’m pretty sure he’s already given up. It just went over his head.
Then he exhales. "Fine," he says. His low-key, resigned tone tells me he didn’t expect this to be that complex.
I’m almost sure he read it on some little website for people obsessed with logic puzzles, but Blue’s answer went too deep, and Marcel lost his footing.
Blue’s mouth curves, barely.
"Fine?" he replies. "You dressed it up to look harder than it is, and in the end you fell short yourself."
A second passes, and Marcel doesn’t answer right away, which is answer enough on its own, but I can see irritation starting to push through his composure.
"That simply was a warm-up for you," he says, suddenly shrugging, changing his tone to something almost light.
Blue tilts his head.
"I don’t need warm-ups," he replies. "If you’re trying to build momentum, you’re wasting it."
Suddenly, a voice comes from beside the wall.
"How much longer is this bullshit going to go on?!"
Gunman is clearly fed up. He would probably prefer actual killing over this ornamental counting, like many other scumbags akin to him, but oh well. He has to listen now to a college activist turned psycho case.
"Shut the fuck up, idiot," Marcel growls, clearly not willing to deprive himself of the pleasure of this twisted game.
He curls his upper lip almost like a growling alpha, fixing Gunman with a heavy stare. In my judgment, Marcel is walking a thin line here. Messing with NFH combatants for his own pleasure seems like a fatal move, but it’s his call. While two dogs fight, a third gets the bone.
Slowly, Marcel turns back toward Blue.
"I can give you that. You know your way around numbers. So let’s make it less pure math and more… my thing."
He takes a deep breath.
"A hundred prisoners. A hundred boxes. Each box contains a number from one to a hundred, placed randomly. Each prisoner can open fifty boxes. They can’t communicate. If every prisoner finds their own number, they all go free. If even one fails, they all die."
I feel the shape of it even if I can’t solve it right away. Something about it sits wrong in my head and refuses to settle.
"What strategy gives them the best chance?" Marcel asks.
I expect Blue to think for at least a moment, to take a breath or shift even slightly, but he doesn’t give Marcel that satisfaction.
"Follow the permutation cycles," Blue says, like he’s correcting something obvious. "Each prisoner starts with their own number and keeps opening the box indicated by what they find, and that gives you a success rate of a little over thirty percent."
