The treasury was more boring than Nyssa had imagined a treasury could possibly be. It was bare of jewels and gold, empty of art and rarities. It just contained eighty-two thousand five hundred and seventy-seven dollars in bills, neatly stacked and wrapped in paper; a few rolls of each denomination of coin; and a lot of pieces of paper stating that the Crown was the owner of so many shares of this company and the deed of that parcel of land and such and such a suite of accounts at Fog Bank.

"Why don't you have piles of silver and gems and stuff?" she asked the Minister of the Department of High Fidelity Storage.

"That wouldn't be very logical," he replied. "The economists at the University of Deductive Ratiocination tell us so, based on their models."

"Oh. It's less interesting, though."

"I'm afraid I don't see what would be interesting about piles of silver and gems," said the Minister, moving on to the armory. Instead of swords and shields and bows, it had...

"Pencils?" said Nyssa. "And calculators?" They were very nice pencils, all kinds both mechanical and conventional, and they looked very sharp, with the really good kind of erasers too, but they were still pencils. The calculators were lovingly encased in screen protectors and covers to defend them from impact, and they were the programmable kind with graphing capabilities, but even so.

"Well, you can count on your fingers, but doing scratch work is more effective," said the Minister of the Department of High Fidelity Storage. "And if you're not unusually good at calculating in your head, you'll find you get better results with writing the problem down or putting it into the calculator. They're a force multiplier, if you'll pardon me my little joke! So of course we keep them in the armory."

"Aren't calculators sort of cheating?" she asked.

"No, of course not," said the Minister. "Everything is just a matter of putting together the right questions. When you've done that, thinking logically self-assembles."

"I've never really studied logic," Nyssa confessed. "Is it just a kind of math?"

"Math is a kind of logic!" corrected the Minister. "Logic is really very simple. Suppose you know that snow is white."

"I do know that snow is white," said Nyssa.

"And suppose furthermore that you know that if there's some thing - such as snow - which is white, then there exists a white thing!" continued the Minister delightedly.

"That seems obvious," Nyssa replied.

"Then from knowing those two things, you can conclude that there is a white thing!" he exclaimed.

"How is that useful?" Nyssa asked.

"Oh, there's a lot of different little steps you can take like that," he said. "But if you take enough little steps, soon you'll find you've gone miles and miles and proven things that would have sounded very silly if you hadn't gotten there in the littlest tiniest increments, where you stop to demonstrate for sure that it's the same whether you say 'trees and bushes' or 'bushes and trees'."

"Why does it matter which direction you say it in?" asked Nyssa.

"It doesn't!" he said. "It matters not one bit, and we can prove it!"

Nyssa giggled at his enthusiasm. "Is that a lot of what you do in the halls of study and research?" she asked, for they'd reached these.

"Yes, it is! Of course much of the research is conducted in the University of Deductive Ratiocination but we have a room for it here, for those of their graduates who wish to serve the Crown."

"What does deductive ratiocination mean?" asked Nyssa, pronouncing the words carefully.

"Deductive means using all those simple little rules and nothing else to get your answers," said the Minister, "and ratiocination means reasoning in an exact manner."

"Can I see the throne room?" Nyssa asked.

"You can, but first! The banquet!" cried the Minister, for at that moment a chime sounded throughout the palace to alert everyone that it was dinnertime. Nyssa followed the Minister; he presently joined up with the other two ministers and they all walked in lockstep through hallways and up and down stairs until they had reached the banquet hall.

In the hall were dozens of people seated all up and down a long table, many more or less human beings but a few puddings and some creatures of intermediate strangeness too. The ministers and Nyssa took four seats close to the end with the tallest, fanciest chair; Pomodoro continued to sit on Nyssa's shoulder. There was a hubbub of conversation - the ministers weren't speaking, but they were exchanging meaningful looks, no doubt deriving what they would each be saying if it weren't too noisy in the room to speak - and then everyone fell silent at once. A heavy door at the far end of the room opened to the sound of trumpets. And in strode the Queen.

The Queen was about as old as Nyssa's grandmother, and much shorter and rounder. She trailed behind her a long lacy train decorated with letters and symbols like the kinds on the flags and in the kitchen, and under it wore a gown beaded all over with tiny spheres, held on with cunning tiny nets of thread since the spheres did not have any holes to put needles through. She looked, Nyssa thought, almost like a drawing: although she wasn't cartoonishly flat or even unblemished, all of the angles of her face seemed very exact, like they had been put there because they belonged there and not because they grew that way.

The Queen took her seat at the head of the table in the tallest fanciest chair and clapped her hands. All of the other doors in the banquet hall burst open, and the servants spun in carrying trays heavy with the local cuisine. Nyssa saw letters and numbers, and long strings of S followed by 0 that were piled like pasta on plates. There were arrows and the three-lined biconditionals and dots and plus signs, and As and Es that the cooks were very careful to place upside down and backwards relative to their diners. The centerpiece of the whole table was the huge roasted square, but it was placed on a tall pedestal in the middle of the table so no one could serve it yet without getting up from their chair. Perhaps it was a dessert.

The Ministers all stood in unison. "Her Majesty, Queen Qed, monarch in Ference and sovereign of the Realm of Possibility, welcomes you all to her banquet. Please enjoy your meals." Then they sat back down and looked at the Queen and she nodded approvingly at them.

Nyssa watched what everyone else was doing and served herself a little of everything, since it all smelled fantastic. She offered Pomodoro tastes of the meal; despite having no mouth, it accepted one long pasta-string of SSSSSSSSSSSSSSSSSSSSSSSSSSSSSS0 and said that was quite enough for it of conventional food, leaving Nyssa with a heaping plate and enough appetite to match. She asked the nearest Minister - she was beside the one belonging to the Department of Accurate Reckoning - what each thing was, and tasted them as she learned their names: stir-fried mixed variables, cream of conditional soup, modus tollens cookies. Whenever Nyssa thought she was too full to eat any more, someone passed around a plate of negation introductions and she'd nibble one of those till she was ready for more biconditionals. At last someone sliced the square into smaller squares, carefully exact. Each guest ate one, and it was the most satisfying dessert Nyssa had ever had. She felt as though she would never need to eat again. She sat back and petted Pomodoro and waited to see what would happen next.

The Queen got to her feet. "My friends, subjects, and guests, thank you all for joining me. Premises, derivations. Subderivations! In conclusion, we in Ference must remain fenced off. Thank you."

And she sat. Everyone applauded. Nyssa clapped too, but didn't know why; that had been the least enlightening speech she'd ever heard. When the Queen strode out and the crowd began to disperse, she leaned over to the Minister beside her and said, "What did that mean?"

"Oh," he replied, "most of us have been here so long that she can cut the speeches way down. They used to be thousands of lines long, but none of us have left town in many years now, and we all know what the premises are and the steps to the conclusions. She only bothered to say what the conclusion was because you're here, probably."

"Gosh," said Nyssa. "Is the fence - new? I thought it was just part of the city."

"It's not very new," he said, as servants took the plates and platters and utensils and napkins away and whipped the tablecloth from the table. "It was put up to defend ourselves against the people of Percepolis, who became hostile when the Princess was banished. Fenced off, only things that meet our standards for introducing new propositions and personages can get in Ference."

"I came over the fence," said Nyssa, "I didn't solve the puzzle, is that all right?"

"Well, it's unconventional," said the Minister. "I'm sure you can get it sorted out, we'll just have to show you to the Bureau and get all your paperwork handled." And he took Nyssa by the hand and led her away from the banquet hall.