Palamedes shrugged. “Nothing. I mean, you can do the challenge, but you get nothing at the end of it.”
Jeannemary said, “So it’s just a huge waste of time,” and Gideon could not imagine how she’d have felt after the avulsion room if the plinth at the other end had been empty.
“Sort of. The challenge itself is still—instructional. It makes you think about things in a new way. Right, Nonagesimus?”
“The challenges so far,” said Harrow carefully, “have encouraged me to consider some … striking possibilities.”
“Right. But it’s like—imagine if someone showed you a new sword move, or whatever, but then you never actually got to sit down and read up on how it worked. It might give you ideas, but you wouldn’t really learn it. D’you follow?”
Jeannemary, Gideon, and Camilla all stared at him.
“What?” he said.
“The Sixth learns sword-fighting out of a book?” said Jeannemary, horrified.
“No,” put in Camilla, “the Warden just hasn’t been to Swordsman’s Spire since he was five and got lost—”
“Okay, okay!” Palamedes put his hands out. He was still holding the bloodstained spectacles. “That was clearly an inapposite comparison, but—”
“A challenge taken purely as a necromantic exercise,” said Harrow calmly, “suggests many things, but reveals none. Only the underlying theorem can lay bare the mystery.”
“And the theorems are behind the locked doors,” Isaac said meditatively, “aren’t they? You need the keys for the doors, or you’re screwed.”
Everyone’s attention was on the two shitty teens. They both looked back, with no small scorn, all grief, uncombed hair, and stud earrings. “We know about the doors,” said Jeannemary. “We’ve seen the doors … and people go through the doors … Well, what else could we do?” she added, somewhat defensively. “If we hadn’t been trailing everybody it would have been that creep Ianthe Tridentarius. And she’s stalking everyone. Believe me.”
（“And trailing differs from stalking how?”
“Because the Fourth doesn’t stalk?”）
“Nothing was preventing you from getting your facility key,” said Palamedes.
Isaac said emptily, “Abigail said—to wait for her.”
Gideon did not know how much the Sixth knew about the keys they’d amassed so far, or what they’d learned of the labs and the studies, how much they knew of the theorems. Palamedes was nodding, thoughtful. “Well, you’ve come to the right conclusion. Behind the doors there are studies, and all eight—there’s eight, obviously, one per House—contain notes on the relevant theorem. All eight theorems presumably add up to some kind of, ah…”
“Megatheorem,” supplied Isaac, who, after all, was like thirteen.
“Megatheorem,” he agreed. “The key to the secrets of Lyctorhood.”
Jeannemary Chatur’s brain had obviously ground forward, struggling past confusion and puberty hormones to some slowly formed conclusion. “Wait. Go back, Sixth House,” she demanded. “What did you mean by one more key?”
Palamedes drummed his fingers on the table. “Well. Forgive me the explanation, Ninth, I know you’ve been keeping track of the keys—” （Ha! Ha! Ha! thought Gideon. She hadn’t.） “—but I couldn’t work out how many keys Lady Septimus had. I knew she had at least one, but when Octakiseron convinced her to hand them over”—he freighted convinced with such heavy scorn it ought to have fallen through the floor—“he accidentally showed us her card. She had two. That means there’s one left that I haven’t accounted for, and we’ve got to account for it.”
“We need to find the Seventh cav,” added Camilla.
He nodded. “Yes, and we also have to work out who the hell’s in the incinerator. Ianthe Tridentarius was right—a sentence I don’t like saying—in that there’s more than one person in there.”
Isaac said: “I have a duty to find out who killed Magnus and Abigail, first and foremost.”
“You’re right, Baron Tettares,” said Palamedes warmly, “but trust me, I think answering those three questions will help us quite considerably in solving that mystery. Ninth, Protesilaus was still down in the facility as of last night.”
Harrow looked at him blankly. “How do you know?”