Escape From the Library

At 8 o'clock in the morning, the examination room for the compulsory course "Prime Number Maze" of the School of Mathematics opened.

The four of Yue Xingwen were instantly pulled into a strange maze.The room in the labyrinth is a cube structure. The six walls of top, bottom, front, back, left and right are all painted with special black paint, and decorated with many stars, just like being in a dark, deep cosmic starry sky. Those "stars" gave off a faint light, illuminating the room.

There is a door on each of the four walls, and four number cards are pasted on the door with white fluorescent characters. The cards are shiny, like the score cards of the "Orienteering" course, which can be taken down and collected.

Additional question: Collect all twin prime numbers.

They should take down all the "twin prime numbers" cards pasted on the wall to complete the additional questions.

Yue Xingwen looked around quickly. The four numbers in the first room were very simple, 4, 5, 6, 7.

Ones prime numbers are easy to find, and 5 and 7 are a pair of twin prime numbers.If you take the wrong card, you will definitely not get points for the additional questions, so you must figure it out before taking the card.

Yue Xingwen looked at Jiang Pingce: "The 3-credit labyrinth class shouldn't be too easy, right?"

Jiang Pingce frowned and thought for a few seconds, and said: "Each room has 4 doors. If there is a passage behind each door, then the number of doors in this maze is 4 to the nth power. The difficulty is not to find twin prime numbers , is to find the correct path. We need to draw while walking the maze, and judge the direction clearly.”

Ke Shaobin quickly took out his laptop: "I can write a piece of code, quickly calculate which are prime numbers, and build a maze model diagram by the way... Wait, my laptop doesn't seem to be able to turn on?"

Liu Zhaoqing went over to have a look: "Is it not broken?"

Ke Shaobin put his fingerprint on the power button and pressed it for a long time, wondering: "Aren't you allowed to use the computer?"

Yue Xingwen helped his forehead helplessly: "It seems that this exam can't be calculated by computer, we have to calculate it ourselves." He looked up at the countdown timer in the upper right corner: "The exam time is 4 hours, if there are many forks, we will take it slowly." Should there be time for investigation?"

Liu Zhaoqing spread his hands: "I haven't touched mathematics for many years, let me do division, my mind is muddled. In this class, you can treat me as a mobile pendant, and I will quietly follow you of."

Yue Xingwen smiled and said, "I'm almost the same."

Jiang Pingce suddenly said solemnly: "In order to pass the customs as soon as possible, we still have a team to explore the way."

Ke Shaobin and Liu Zhaoqing looked at each other and said in unison: "Squad?!"

He must be on the same team as Yue Xingwen, can the other two do it?

Ke Shaobin adjusted his glasses in embarrassment, and his ears were slightly red: "Although I am a science student, I... have been used to using computers to solve all calculation problems since my freshman year. I haven't done math by myself for a long time. Three For multiplication and division with more than a few digits, I have to use a pen and paper to calculate it several times before I can figure it out. I am on the same team as Senior Brother Liu, so the efficiency may be very low, right?"

Jiang Pingce said: "It's not divided into two teams."

He turned his head to look at the teammates around him, and said word by word: "It's divided into four teams, and everyone is in one team."

Three people: "..."

are you joking?Liu Zhaoqing looked terrified: "I'm really bad at math!"

Yue Xingwen quickly understood his train of thought: "You mean, the four of us go to explore the road separately, and all the calculation tasks are entrusted to you? Do you calculate the prime numbers of the four roads at the same time by yourself?!"

Sure enough, Xingwen knew him better, Jiang Pingce nodded calmly.

Ke Shaobin and Liu Zhaoqing stared at him with wide eyes.

I thought that the team he was talking about was divided into two teams, but in the end, Jiang Pingce was more ruthless than everyone imagined-directly divided into four teams!He counts four ways at the same time by himself!

Obviously, he has enough confidence in his calculation ability.

Jiang Pingce looked at Yue Xingwen and said seriously: "The research group channel can send messages during the exam period. Every time you enter a maze room, you will type the number on the door on the research group channel. I will calculate and give the correct answer. .”

Yue Xingwen tried to post a line on the research group channel: "Can you see it?"

All four of them saw the information in the transparent floating frame in the upper left corner.

Yue Xingwen's eyes lit up: "This method is amazing! Four people walk forward in four ways, which can greatly save the time of exploring the maze, and the number of times of going back and forth will be reduced." He paused, a little worried Looking at Jiang Pingce cautiously, "But in this case, you will be under a lot of pressure, right? Four roads, if you get confused in the back, can you tell the direction?"

If Jiang Pingce's judgment is correct, there are four doors and four paths in each maze room, then there are as many correct paths as 4 to the nth power, can he remember the exponentially increasing paths?

Jiang Pingce looked at Yue Xingwen, his black eyes were full of seriousness: "Trust me."

Meeting his gaze, Yue Xingwen immediately nodded flatly: "Okay, I believe you, and I will do as you say!"

Jiang Pingce said: "Take out your dictionary first, tear some paper for me, and I will draw a map of the maze path."

Yue Xingwen did as he did, and took out a pen from his pocket and handed it to Jiang Pingce.

Jiang Pingce walked to the wall with the number [5] on it, pushed open the door, and the next room was exactly the same as this room, with four walls and four numbers on it.

Jiang Pingce tried to open the other three doors [4], [6], [7] and came to the same conclusion.

Prove his deduction is correct - every room has four doors and four exits.Some of the rooms in the back are sure to become dead ends.If you want to find the correct exit of the maze, if the four of them are together and go through each room slowly, of course they can get out in 4 hours. However, if you want to get a high score in this class, you must not use this The most stupid way.

Jiang Pingce quickly drew a few squares on the paper, and explained: "Everyone has walked too many paths, and they will not remember the direction clearly. For example, the four numbers 4, 5, 6, and 7 in the current room, push away and write [ After the door of [5], you will enter the next room. Remember the number of the other door connected with [5]. When counting, start from the door you walked in, and follow The hour hand counts, understand what I mean?"

Yue Xingwen saw that he drew five consecutive rooms on the paper, all of which were squares, with a number on each side. As he said, if there are too many paths behind, the sense of direction will become clouds, east, west, north, south It must be hard to tell, not to mention that all the walls inside this maze have been painted into a starry sky, so it's strange not to be dizzy.

If you want to locate the exact direction, you must use the room of the previous maze.

For example, the door directly in front of room a is attached to [5], which is regarded as [door 5]. After opening this door, it is room b. Since room b is also a square, two squares will share a side when connected together. That is, the four walls of room b must have a door directly connected to [door 5] of room a.

The logic used by Jiang Pingce is that "the two rooms share a door, and different numbers are pasted on the front and back of the door."Then, starting from the first room, and continuously reasoning down, a complete maze graphic can be launched.

This method of reasoning does not need to care about east, west, north, south, as long as every room is correct, his diagram will not be wrong.

Jiang Pingce looked at the three teammates and reminded him again: "Be sure to remember the number on the door you pushed open. When you enter the next room, immediately look at the number on the back of the same door, count clockwise, and don't make mistakes. If you make one mistake, there will be a series of mistakes in the future, do you understand?"

The three looked at each other and nodded in unison: "Understood!"

They can't tell the difference between east, west, north and south, but they can tell clockwise and counterclockwise!

Jiang Pingce said: "Get ready to divide into teams. Mr. Ke will go to gate 4, I will go to gate 5, Xingwen 6, brother Liu 7."

Yue Xingwen stretched out his hand: "Come on, let's cheer for Xueba."

Liu Zhaoqing and Ke Shaobin put their hands up consciously. Jiang Pingce glanced at Yue Xingwen and put his hands up in cooperation. Yue Xingwen gently covered the back of his hand with the other hand, smiling brightly: "Come on, Don't put too much pressure on yourself, as long as we can pass the test, there is no need to go to No.1, you know?"

Jiang Pingce's heart warmed, and he nodded towards him: "Well, everyone, don't take the wrong cards. The scoring standard for the additional questions must be that all the cards we collect must be twin prime numbers, and points will be deducted for wrong ones."

The four people looked at each other and walked through the four doors separately. Numbers appeared again in the next room.

This time it's double digits.

越星文的房间是11、12、13、14；柯少彬的房间16、17、18、19，刘照青则是28、29、30、31，江平策是40、41、42、43。

The two-digit number is very simple, and everyone can calculate it by themselves, but for the convenience of Jiang Ping's planning, the three still followed the rules he said, counting clockwise from the door they entered.

Jiang Pingce gave instructions: "Take down the twin prime number card, Xingwen goes 13, Ke Shao 18, brother 30."

He always chooses the road directly in front of him. He first walks in a straight line, and when he encounters a dead end, he retreats to the right and then to the left, so as not to mess up.

The four quickly entered the next room, and this time the number became three digits.

Jiang Pingce: "Brother, take 107 and 109, and go through the door of 111."

According to his instructions, Zhao Qing took down two number cards and continued to move forward.

The channel of the research group keeps popping up messages from Jiang Pingce: "Xingwen takes 137, 139, go 133."

"Ke Shao takes 179, 181, and walks through door 181."

In the next room, the prime numbers turned into four-digit numbers again.

Everyone can do the math for two-digit and three-digit numbers. After reaching four-digit numbers, the three of them simply gave up thinking. If they have time to do the math slowly, they might as well type quickly and wait for Jiang Pingce's results.

Jiang Pingce's brain speed is astonishing, and he can calculate four paths at the same time and can give the answer in seconds!

“4019，4021”“8969，8971”“9281，9283……”

Walking through another room, the number has risen to five.

"16829, 16831" "31541, 31543..."

But for Jiang Pingce, the five-digit number is not difficult, and he reported a pair of twin prime numbers quickly and accurately.

Teammates are collecting more and more prime number cards.Jiang Pingce not only has to calculate the twin prime numbers of the four roads at the same time, but also draws the maze path while walking to ensure that the direction of his teammates is not wrong...

In this maze full of numbers, other people's eyes were darkened and they didn't know how to move, but Jiang Pingce was like a fish in water—these numbers were his closest partners since he was a child.When he was in high school, he participated in the national mathematics competition. He liked mathematics from the bottom of his heart, and liked the wonderful, rich and rigorous world made up of numbers.

In the world of mathematics, he is like a natural king. Others are afraid of numbers, but he can control them.

The numbers in the room are getting more and more complex, and the amount of calculations is increasing crazily.

Jiang Pingce is like a high-speed computing machine in his brain. While calculating, he gradually draws a maze in his mind. As soon as his teammates type the numbers, he can always give the correct answer immediately.

Yue Xingwen: "The room in front is a dead end, there is no door."

Jiang Pingce instructed: "Go back one room and walk through door 8861."

Ke Shaobin quickly said, "I have encountered a dead end."

Jiang Pingce: "Back back, go to gate 9657."

"Brother, come back, door 9861."

Under Jiang Pingce's command, everyone explored the way repeatedly, and the entire mathematical maze was explored with almost countless forks. Yue Xingwen alone took eight forks. It is hard to imagine that Jiang Pingce did not make mistakes.

They thought they would be able to check all the forks in this way. However, when the number of twin prime cards collected by Yue Xingwen reached 30, a message from Liu Zhaoqing suddenly appeared on the channel of the research team: "I rely on , there was an elevator in the room I entered, and there were buttons for up and down."

Within a few seconds, Ke Shaobin also sent a message: "I entered the door of 24189, and there is also an elevator inside."

An elevator that can go up and down?

Yue Xingwen said: "Could it be that this maze has at least three floors?"

Jiang Pingce said: "I have expected it a long time ago. The course description says that this is a three-dimensional maze. No matter how many forks there are in the flat maze, it is not difficult to make marks and explore slowly. The difficulty of the three-dimensional maze will be doubled."

Yue Xingwen worried: "Three-dimensional maze, your calculation amount will be doubled, right?"

Jiang Pingce said: "It's okay, go back first, we have collected all the twin prime numbers on this floor before going upstairs."

If they want to do additional questions and collect all the twin prime numbers, it means that they must explore all the rooms in the maze.The three of them were already dizzy and couldn't tell the north from the south, but Jiang Pingce's calm and clear command gave them full confidence.

In this vast digital maze like the starry sky, not only four lines of simultaneous calculations are required to allow teammates to quickly find twin prime numbers among the densely packed numbers, but also to ensure that teammates do not get lost in the process of repeatedly pushing doors, exploring paths, and returning.

With such a difficult command, other teams may not even dare to think about it.

But Yue Xingwen believes that Jiang Pingce can definitely do it.