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?”

“We saw him go in,” said the Fourth as one. And Isaac added: “After we eavesdropped on you and the Sixth.”

“Good for you. But it makes sense, too. Lady Septimus said He didn’t come back, and when we saw her key ring just now it only had challenge keys—no hatch key. She must have given that to him so he could access the facility by himself—although why, I still don’t know. I bet you the whole of my library’s physical sciences section that he’s still down there. It would be impossible for someone to bring him up without being seen.”

“Then we need to go down and look,” said Jeannemary, visibly impatient at the lack of action. “Let’s go!”

“Don’t be so Fourth,” said Palamedes. “We should split up. We’re fighting a battle on two fronts here. Frankly—I would not leave Lady Septimus unguarded, sans cavalier, with just the First House to guard her.”

Harrowhark said, “Her keys are gone. What’s the attraction now?”

Camilla said, “Vulnerability.”

“Yes. It can’t just be a game of keys, Nonagesimus. Why did Magnus Quinn and Abigail Pent die, when they had nothing on them but a facility key and their own good selves? Why has Protesilaus gone missing, when the most he would have had was his facility key? Is he still down there? Who died before this challenge even began? And then there’s the issue of the other Houses. I do not know about you, Reverend Daughter, but until Cam’s healed up, I plan on wetting myself lavishly.”

Isaac gave a rather lame and high-pitched giggle. Camilla said gruffly: “Warden, it’s just my right hand—”

“Hark at her! Just your right hand. My right hand, more like. God, Cam, I’ve never been so scared in all my life.”

Harrowhark ignored this cavalier-necromancer banter and cleared her throat, pointedly. “Septimus wants guarding. Her cavalier should be found. What do you suggest?”

“The Fourth House stays with the Lady Dulcinea,” said Palamedes, slipping his glasses back over his long nose. “Gideon the Ninth stays with them as backup. You, I, and Camilla go down to the facility and see if we can locate Protesilaus.”

There was more than one bewildered stare aimed his way: his own cavalier looked at him as though he had taken leave of his senses, and Harrow yanked her hood off her head painfully as though to relieve her feelings. “Sextus,” she said, as though to a very stupid child, “your necromancer is wounded. I could kill the both of you and take your keys—or just take your keys, which would be worse. Why would you willingly put yourself in that position?”

“Because I am placing my trust in you,” said Palamedes. “Yes, even though you’re a black anchorite and loyal only to the numinous forces of the Locked Tomb. If you’d wanted my keys through chicanery you would have challenged me for them a long time ago. I don’t trust Silas Octakiseron, and I don’t trust Ianthe Tridentarius, but I trust the Reverend Daughter Harrowhark Nonagesimus.”

Beneath the paint, Gideon could see that Harrow had changed colours a number of times through this little speech. She went from being a rather ashen skeleton to a skeleton who was improbably green around the gills. To an outsider, it would have just been a blank Ninth House mask twinging from darque mystery to cryptique mystery, giving nothing away, but to Gideon it was like watching fireworks go off.

Her necromancer said gruffly: “Fine. But we’ll watch over the Seventh House. I’m not going down the ladder with your invalid cavalier.”

Palamedes said, “Fine. Perhaps that’s better use of our talents, anyway. Fourth, are you all right to go with Gideon the Ninth? I realise I am presupposing that our motives all align—but all I can assure you is that they really do. Search the facility, and if you find him—or come up short—come back to us, and we’ll move from there. Get in and get out.”