He wouldn’t break down, wouldn’t crack.
Never.
Vaughn had seen Darnell run a sixteen-hour interrogation by himself without so much as a break for a drink of water. Went against every rule the PPD had, but their suspect had eventually confessed.
“It’s effectively zero,” Ivy said. “The probability of all one hundred prisoners finding their number is zero.”
“Well, I take back my previous answer. I’ll take my chances behind bars.”
Darnell’s secondary power was humor. And his damn hunches—Vaughn couldn’t forget those, either.
“But there weren’t one hundred boxes or one hundred prisoners. There were only ten,” Vaughn said, trying to get them back on track. “And they weren’t prisoners.”
Until they were.
The digital locks on the doors in the barn flashed in his mind.
“The odds improve with fewer participants.” Vaughn noted that Ivy wasn’t viewing them as victims anymore. Ivy had turned this into a true math problem, her way of dissociating herself from the image she’d seen on his phone. “But the probability of success is still only 0.1 percent with ten prisoners.”
“What’s with the—”
Vaughn wanted to say prime numbers, but Ivy wasn’t done yet.
“But that’s only if each contestant opens random boxes. If all of the prisoners utilized a permutation approach, they can vastly improve their odds of success.”
“Permutation approach?” Darnell asked.
“Yeah, it’s simple, really. Say you’re prisoner number three. The first box you should open is the third one. Find your number by sheer chance? Great. You’re done. If you don’t—instead, you find number seven inside, for instance—then you go to the seventh box. Open that box. Repeat.” Ivy drew a small circle in the air with her finger. “You form these permutations or loops. Using this strategy can vastly improve your odds. In the ten prisoner scenario, the odds of being successful goes from 0.1 percent to about 36 percent.”
“36 percent?” Darnell was legitimately surprised, but him pretending to understand was a farce.
Ivy nodded.
“Yep. About a third of the time, you can beat the game.”
Darnell whistled, laying it on thick.
“But the numbers aren’t one to ten,” Vaughn remarked. “They’re prime numbers.”
“Doesn’t matter what the numbers are. Could be random, could be prime—as long as they’re all the same, you can create loops. I’m guessing that’s why the numbers were on the outside of the box, so that the contestants could follow the permutation approach.”
Vaughn thought about Aaron Treadman lying on the gurney at the morgue, Dr.Button hovering over him.
Aaron Treadman had a high school education. He’d been a security guard at Princeton, but was unemployed at the time of his death.
Vaughn put the odds of Aaron knowing the “permutation approach” for solving the 100 prisoners problem at pretty close to zero.
One in a...decillion, maybe.
Hey, maybe he wasn’t beyond learning new things.
Darnell shrugged.
“I don’t... really get it, but okay.”
Ivy blushed.
“Sorry, I nerd out sometimes. Math—”
