The Goblin's Puzzle

by Andrew Chilton

  “Why should I?” said Just Alice.

  “Because having a fate, even a bad one, is a gift from the gods,” said the boy.

  “Look, either I have a fate or I don’t,” said Just Alice. “If I have a fate, then that’s what’s going to happen to me, whether I believe it’s my fate or not—”

  “Yes, but—”

  “In fact, it’d be my fate not to believe in fate, wouldn’t it?”

  “No, but—”

  “And if I don’t have a fate, then I’d be wrong to believe that I did,” said Just Alice. “So why should I believe in fate? Either it makes no difference—and I have no choice in the matter—or I’m wrong.”

  “But—but—but—” spluttered the boy. This was blasphemous in so many different ways he didn’t know where to start. “But those who defy their fate are cast into the Pit!”

  “Which, by your lights, would be my fate,” said Just Alice. “As I don’t have any choice in the matter.”

  Mennofar chuckled. “Got you there, hasn’t she?”

  “It doesn’t work like that,” said the boy. It could not.

  “Why not?” said Just Alice.

  Somehow, Just Alice had managed to take a very simple and beautiful truth and make it twisty and complicated. There was a reason she was wrong. There had to be. “I don’t know,” said the boy. “But it doesn’t.”

  “Maybe you were fated not to know,” said Just Alice.

  Mennofar laughed out loud.

  “Stop it!” shouted the boy. “I may not be able to explain it, but I know the truth. It’s wrong for you to make fun of it.”

  She put her hand on his shoulder. Very quietly, she said, “I’m sorry.”

  “It’s all right,” said the boy. It was not. It was blasphemy. But the boy knew that Alice meant well. And he wanted it to be all right.

  “I know I can go on and on, and that gets on people’s nerves sometimes,” said Just Alice. “Still, it’ll do me good if I ever become a sage.”

  “You can’t be a sage,” said the boy.

  She stiffened. “Because it’s not my fate?”

  “Because you’re a girl,” said the boy.

  “Girls can be sages!” said Just Alice. “At least, there’s no rule against it. It’s even happened a few times. I’ve studied up on it.”

  “So you’re an apprentice sage,” said the boy.

  “Er, no,” said Just Alice, and she explained about agons and ordinaries and extraordinaries. “But they won’t invite me. It’s like they’re just pretending girls are allowed.”

  “You have to be pretty clever to be a sage,” said the boy. Even as he started to say it, he knew he should not. Still, he could not seem to stop himself. “Maybe you’re not—”

  “They invite every blockhead boy who even thinks about applying!” shouted Just Alice. “I’m smarter than every single one of them!”

  “I meant to say maybe they don’t realize—”

  “I can prove I’m smart enough,” she said. “Just give me a problem to solve, if you don’t think so.”

  “I’m sure you’re—”

  “Give me one!”

  “Fine. How do I keep both of my promises?” said the boy. If she was going to start solving problems, they might as well be his problems. “How do I defeat the dragon without hurting him?”

  “You’re framing the problem wrong,” said Just Alice. “You promised to rescue the Princess, not defeat the dragon. You just have to trick the dragon and help the Princess escape. That way, you can keep both promises.”

  “Oh,” said the boy. It was a pretty neat answer, really. And an annoyingly obvious one, once she said it out loud.

  “That was easy,” said Just Alice. “Now, have you got a hard one?”

  “I might,” said the boy. There was, of course, no “might” about it. But to explain the problem to her, he would have to tell her about being wrongly enslaved. Still, she might be able to help. In The Tales, there were always parts where the hero stabbed things and parts where the hero figured things out. While he had managed to muddle through his first stabbing part, he had gotten nowhere on figuring things out. “But before I tell you, you have to swear—on your honor—not to tell anyone.” If she would not, it would be a reason not to tell her.

  “I promise,” she said.

  “And you have to promise not to look down on me or make fun of me or be mean to me,” he said.

  “That’s just ridiculous. Why would someone do that?” she said.

  Mennofar did his best to look innocent. The boy just waited.

  “All right. I promise,” she said.

  “I was falsely held as a slave and ran away,” said the boy.

  “That’s terrible,” she said. “Who would do such a thing to you?”

  “Oh, I have no idea,” said the boy.

  “Well, how did it happen, then?” asked Just Alice.

  “I don’t know that, either,” said the boy.

  “Well, if you don’t know—”

  “There’s a story,” said the boy. Then he told her about Casimir’s villa and Tibor’s murder and Mennofar’s rescue and everything else that had happened to him, finishing up with all the yes-or-no questions and the endless scenarios. “Every answer gives me ten more questions. That’s the problem,” said the boy.

  “No, the problem is that you’re thick as treacle,” snapped Just Alice, smacking him on the head for his stupidity.

  The boy said, “But you promised—”

  “You’ve gone about it completely backward. You should be asking the most general questions you can,” said Just Alice.

  “How would that help?” snapped the boy. He was still stinging from the treacle comment.

  “I’ll show you. Pick a number between one and thirty,” said Just Alice.

  “Nineteen,” said the boy.

  Just Alice rolled her eyes and said, “Pick another one and don’t tell me this time.” She paused a moment to let him choose. “Now, how many yes-or-no questions do I need to figure out what your number is?”

  “Thirty,” said the boy. “No, wait, you don’t have to ask for the last number, so it’s twenty-nine.”

  Just Alice said, “No, I need—”

  “Twenty-eight,” said the boy. “You already know it’s not nineteen.”

  Just Alice said, “No, I need—”

  “Wait, you said between one and thirty,” said the boy. “If that means I can’t pick one or thirty, then you need twenty-six.”

  “Five!” yelled Just Alice. “I need five questions.”

  The boy said, “Maybe if you were lucky…”

  “Is your number more than fifteen?” asked Just Alice.

  “No,” said the boy.

  “More than eight?” asked Just Alice.

  “Yes,” said the boy.

  “More than twelve?”

  “No.”

  “More than ten?”

  “Yes.”

  “Is it eleven?”

  “No.”

  “Then it’s twelve,” said Just Alice. “You just cut the possibilities in half each time.”

  “That’s a good trick,” said the boy. “But there’s a lot more than thirty possibilities.”

  “It doesn’t matter. More possibilities means you need more questions, but the number of questions does not go up near so fast as the number of possibilities,” said Just Alice. “Every time you double the number of possibilities, you need just one more question. Up to thirty-two is five questions, while up to sixty-four is six,” she said. “It’s all to do with the powers of two.”

  “I didn’t know about the powers of two,” said the boy. “I thought it was three and seven that were especially magic. What powers does two have?”

  “No, not magical powers,” she said. “Powers of two as in doubling each time. It’s mathematics— Stop that!”

  “Stop what?” said the boy.

  “You’re nodding along the way people do when they don’t want to admit they ha
ve no idea what you’re talking about,” said Just Alice.

  The boy stopped nodding.

  “But you know what mathematics is, right?” said Just Alice.

  The boy said, “Well—”

  “Didn’t they teach you anything at all?” she said.

  “No,” said the boy. “Why would they?”

  “Why indeed?” she asked. “He wouldn’t want a slave who could think, would he?”

  “I can think,” protested the boy. “I’m not soft.”

  “No, I didn’t mean that,” she said. “I just meant that it wouldn’t do for him to give you anything to think about.”

  “Like what?” said the boy.

  “Like why some people are slaves and others aren’t,” said Just Alice.

  “Because slave is the fatestone that the Three Sisters drew when those people were born,” he said, though she had already made her views on fate clear enough.

  “That’s not what I meant,” said Just Alice.

  “Well, what did you mean?” said the boy. “And how did you know which numbers to pick?”

  “What? Oh, you just take half the difference between the two numbers. Halfway between ten and twenty is fifteen,” said Just Alice.

  “And do you memorize those? Because that must take up a lot of your time,” said the boy.

  “Memorize? No, you just add it up in your head,” said Just Alice.

  “You can add like that in your head?” asked the boy, wide-eyed.

  “Yes. Do you have to write it out?” she asked.

  The boy burst out laughing. “I don’t know how to write,” he said.

  “Well then, what do you do?” she said.

  “These days, I rescue clever girls from ogres. Before that, I caught bats for goblins. And before that, I took care of the plants in the inner and outer courtyards,” said the boy.

  “Yes. Of course. Stupid question, really,” she said, mostly to herself. “Anyway, the point is to start broad and eliminate lots of possibilities at a single stroke.”

  “I know,” said the boy. “I can remember that much.”

  “From when? Before you were born?” said Just Alice.

  “Don’t be such a mean-o,” said the boy. “I remember it from when you showed me a minute ago.” He scowled at her. “You think I’m just some ignorant slaveboy, don’t you? Maybe I never did study with sages, but that doesn’t mean I can’t learn something when shown it. I’m not stupid.”

  “I don’t think that,” said Just Alice, sounding as though she might. “Now, if you’re not a slave, then either you were born free or you were born a slave and then freed. So find out which.”

  “I must have been born free,” said the boy. He had an important fate, and there was no way it could be if he were just some freed slave.

  “Just ask,” said Just Alice.

  “Fine,” said the boy. He turned to Mennofar. “I was born free, wasn’t I?”

  Neither of them had noticed that Mennofar was aiming a fearsome scowl at Just Alice or that his skin had turned a green so dark it was almost black. “No,” he said.

  “You got it wrong,” said the boy. “The answer was supposed to be yes.”

  “No, it wasn’t,” said Mennofar.

  “It has to be,” said the boy. “I can’t be a freed slave. I have an important fate. You told me so. Somebody stole it from me and tried to destroy the proof.” He waved the ring. “The only way I have a birthright worth stealing is if I was born free.”

  Mennofar shrugged.

  “Don’t shrug at me,” said the boy. “You’re saying I’m a freed slave?”

  “No, no, no, no,” cried out Just Alice in frustration. “The point is not to waste questions like that. You already know that you are free and that you were not born free. That has—”

  “No,” said Mennofar.

  “—to mean you were freed after you were born. Asking if you were is totally unnecessary and— Wait, did he say no?” said Just Alice.

  “I did,” said Mennofar. He gave her his toothiest smile. His skin shot from near black to a shade of emerald that almost glowed.

  “You said it was about eliminating lots of possibilities,” said the boy. “What happens when you eliminate all of them?”

  “I don’t know,” said Just Alice.

  Just Alice and the boy both studied Mennofar for a long moment. Mennofar just glowed back at them with his happy green glow.

  “He told me once that humans and goblins are too different to ever really be friends,” said the boy.

  “Mennofar, you’re a good goblin. Won’t you give us a hint?” said Just Alice.

  “Doing anything more than holding to my exact word would be a stain upon my honor as a goblin,” said Mennofar. “Besides, your little logic lesson put a big dent in my fun. Why should I give up any more of it?”

  “Rot,” said the boy. “We don’t even know what to ask. You’re having more fun than when I was asking the wrong questions.”

  “That could be true,” admitted Mennofar.

  —

  That evening, they camped only a little ways short of where Ludwig once held Just Alice prisoner. They ate a cold meal and turned in early. Just Alice, however, couldn’t sleep. She lay on her back and looked up at the sea of stars overhead. In the morning, they would rise, and the boy would face a dragon, a dragon he had taken a mighty oath not to harm. A few hours before, that oath had been so important to her, but now it just seemed ridiculous to tie his hands like that. Of course, there probably wasn’t any way he could hurt Ludwig, but she still shouldn’t have demanded it of him. “I’m sorry,” she said in a voice barely above a whisper.

  “For what?” came the boy’s voice back through the darkness.

  “For—I don’t know,” said Just Alice. “For being so bossy. I can’t help it. It just comes over me sometimes.”

  “I don’t think you’re bossy,” said the boy.

  “It’s sweet of you to say so,” said Just Alice. “But I know the truth.”

  “I really don’t,” said the boy.

  Just Alice laughed a little.

  “What’s so funny?” said the boy.

  “It just struck me: how would you even know if I was bossy?” said Just Alice. “You were a slave.”

  The boy shot up. “That’s not true!” he said.

  “No, I meant—”

  “Take it back!” said the boy. “It’s a lie.”

  Mennofar sighed heavily. “I suspect she meant that because you were generally believed to be a slave, you were likely accustomed to being ordered around,” he said. “So it is unlikely that you would be the best judge of whether someone was, or was not, bossy.”

  “Oh,” said the boy, mollified. “That does make sense, I guess.” He lay back down. For a long moment, no one said anything. “I never thought about it that way before,” he said finally. His voice was very quiet. “I guess they did like to give me orders. They sure did it a lot.”

  Just Alice reached out and took his hand in the dark. “I know,” she said.

  “Yes, yes, I am sure it was terrible. Now, will you please go to sleep,” said Mennofar. “You have a big day ahead of you, and you will not want to be tired and cranky when the dragon roasts you alive.”

  —

  In the morning, ten minutes’ walk brought the boy, Just Alice and Mennofar to the strange patch of broken ground where basalt columns reached up toward the sky—the place where Just Alice had been imprisoned only a few days earlier. Sure enough, on top of the tallest column, a pretty young girl was marooned in the wreck of an expensive silk dress. It had been torn by dragon claws, stained with sheep’s blood and generally ruined by a week’s camping in the wild. The three of them crept forward and hid behind a boulder.

  Just Alice peeked over the top. “I don’t see Ludwig,” she whispered.

  “Is it the Princess?” asked the boy.

  “Who else would it be?” asked Just Alice.

  From atop the pillar of stone came a
lordly pronouncement. “Oh, I grow ever so weary of mutton.”

  “She sounds like a princess,” said Mennofar. “And I have known a few.”

  “And did you torture them as bad as you’re torturing me?” asked the boy.

  Mennofar thought for a moment. “Some, yes,” he said.

  Just Alice peered around the rock. “I don’t see him. I don’t think he’s even here,” she said.

  “Then who was she talking to?” said the boy.

  “I don’t know,” whispered Just Alice. “Maybe she’s expecting someone to bring her lunch.” She stood up and surveyed the scene.

  From behind one of the boulders, Ludwig’s head bobbed up. Slowly, the great spade-tipped tail uncoiled. His bat wings unfurled, and when the boulder itself began to rise and turn, she could see it was actually Ludwig’s broad hindquarters. He turned himself all the way around and faced Just Alice head-on. Through all the time she spent with Ludwig, she had never stood on level ground with him. She had never taken in just how big he was. He was bigger than a house, and his claws were the size of full-grown men. Each of his wickedly sharp teeth was the length of her arm.

  “Oh, dear, it’s you, isn’t it?” said Ludwig. “I’m sorry. I was rather fond of you.” Just Alice did not like the way he spoke in the past tense.

  Just Alice drew herself up to her full height, set her jaw firmly and cast a cool eye on Ludwig. “Yes, I am Just Alice,” she said.

  “I thought you were Plain Alice,” said Ludwig, a little confused. “Who changed it?”

  “No one,” said Just Alice. “Er, I mean, I did.”

  Ludwig studied her quizzically. “But it is you, right?” he said. “You are the same Alice I carried off before, aren’t you?”

  “Yes,” she said. “I escaped from the ogre.”

  Ludwig set his head on the ground and put his two front paws on his snout. “That is good,” he said. “But why did you come here? Couldn’t you just have gone home?”

  “Not while you still hold the Princess,” said Just Alice.

  “Who?” said Ludwig.

  “The Princess. Up on the stone pillar. The other Alice,” said Just Alice.