Xueba starts with change
Chapter 505 That fatal flaw!
Chapter 505 That fatal flaw!
Princeton is probably best known to the world as Princeton University and the Princeton Institute for Advanced Study.
Because there have been too many scientific masters here.
Including now, here is also the center of mathematics in the world.
Anyone who is a well-known scholar will probably be inextricably linked with this place.
Today's Princeton welcomes many "outsiders" of different skin colors, different countries, and different occupations.
And the reason why everyone came here today is only for one purpose.
That is what will start tomorrow, this world-renowned report meeting.
They are all looking forward to the "wonderful duel" between Chen Zhou and Harold Hoofgot starting tomorrow.
I am also looking forward to the Goldbach conjecture, which originated in 1742, challenged mankind for nearly three centuries, shocked the world many times, exhausted the energy of many of the most outstanding brains of mankind, and also fascinated thousands of amateurs. its end result.
In short, this will definitely be a report meeting destined to be recorded in history in the 21st century.
Although the content of the report meeting starting tomorrow, only a very small number of people can understand it.
But that doesn't stop others from coming here to witness a truly meaningful moment they've been looking forward to.
Take the brother on Chen Zhou's Weibo who said he wanted to broadcast live. What he wanted was to witness this historic moment with his own eyes and record it with his own hands.
At this time, the old man had also arrived in Princeton, and was guarding the entrance of the hotel where the report was held.
For nothing else, he just wanted to cheer Chen Zhou with the blessings of countless netizens.
He hoped that Chen Zhou would leave the right to prove Goldbach's conjecture, which Hua people have been thinking about, in the hands of Hua people.
However, he waited until the sky darkened, but he didn't see Chen Zhou.
He can guarantee that he will never miss or let go of anyone who looks similar to Chen Zhou.
However, Chen Zhou was not seen appearing.
In desperation, he could only return to the hotel where he lived, quietly waiting for the report meeting tomorrow.
In fact, Chen Zhou did pass in front of this old man.
However, Chen Zhou was wearing a hat, and the brim of the hat was pushed down extremely low.
Except for Professor A Ting and others who were with him, no one else knew that the person wearing the hat was Chen Zhou.
Because of this, this old man with good wishes didn't find Chen Zhou.
As for Chen Zhou, since entering the hotel, he has been in the room and never came out.
He is replying to the reviewer's email.
In the email, there are some questions raised about the paper.
Although the report meeting is about to start, the length of the report meeting is considered.
It is impossible to put all the problems in the report meeting.
Therefore, these reviewers sent some questions to Chen Zhou by email.
Chen Zhou was so happy, at least he didn't have to worry about being recognized when he went out.
Then lead to some unnecessary troubles.
In this way, staying in the room, while answering emails, you can also organize your own thoughts.
Find some details that may be overlooked by yourself.
Be fully prepared for the report meeting that starts tomorrow.
Speaking of which, Chen Zhou's paper reviewers are all his "old friends".
Among them, there are three mathematicians, Faltins, Deligne, and Langlands, who are in charge of reviewing his paper on the proof of Kramer's conjecture.
While Chen Zhou was answering the questions in the email, Faltings and the others were also carefully reviewing the paper.
"Deligne, how is the progress on your side?"
Faltings glanced at the person sitting not far away, and gently squeezed the center of his brows.
Deligne, who heard the voice, turned his head and glanced at Faltings, and replied: "My side is going well, and he answered all the questions sent to Chen Zhou. It won't take long. The responsible part should be able to complete the preliminary review."
After a pause, Deligne smiled again and said, "However, I don't think your condition is very good. I think you probably need a bottle of German stout now to refresh yourself."
Faltins let go of the hand pinching his eyebrows, and shook his head helplessly at Deligne: "After all, I am getting older, and my thinking is not as active as when I was young..."
Deligne put away his smile, nodded slightly, and said with emotion: "As we grow older, although we have richer knowledge and experience, we have gradually lost the active thinking that is most needed for mathematical innovation. , we are all old..."
"Mathematics has always been dominated by young people, and the future belongs to these young people." Faltings finished speaking, put down the pen in his hand, gently closed the typed draft of the thesis, got up and said to Deligne, "Go Well, just as you said, let's go drink some beer first, and then come back to continue."
Deligne was stunned for a moment, and then teased: "Aren't you afraid that the brains of the elderly will completely lose their sensitive thinking ability due to alcohol paralysis?"
When Faltings heard the words, he immediately stared and said, "Are you going?"
"Go, go..." Deligne said quickly, "As long as it doesn't affect the normal progress of tomorrow's report meeting..."
Faltings, who was holding his coat, heard the second half of Deligne's words. He glanced sharply at the printed manuscript on the table, and said softly: "I have prepared the questions that should be asked. .”
Deligne raised his head slightly and glanced at the German old man.
Faltings also happened to look up and look at the Belgian Viscount.
The two smiled at each other.
Even though they are really old, these days, they have really worried a lot about the review of Gechai's proof paper.
However, they are extremely serious about Goldbach's conjecture.
This is also the attitude and the most basic respect for a nearly 300-year-old mathematical problem.
In any case, the proof of Goldbach's conjecture wants to be recognized by the entire academic community.
You have to get past them first.
For the report meeting that starts tomorrow, they won't release water.
Like Faltings and Deligne, there are Langlands, Fefferman, Wiles and others.
They also encountered a lot of trouble when reviewing the manuscript.
Just like Wiles' paper proving Fermat's last theorem, for the papers of Chen Zhou and Harold Hoofgot, they also carefully checked every logical link of the part they were responsible for.
If the paper itself cannot be logically self-consistent, then there is no need to continue the review.
But this is an extremely exhausting job.
This kind of consumption is not only reflected in time and details, but also in the content of the paper itself.
The two papers are a melting pot of mathematical tools and ideas such as sieve method, circle method, density ratio method, and distribution deconstruction method.
I want to completely clarify the relationship between these mathematical tools, especially Chen Zhou's distribution deconstruction method, which was born not long ago.
Its difficulty can be imagined.
Although due to the particularity of the paper, the reviewers can throw questions to the contributors at any time in order to get answers.
However, there is always a process of discovering and asking questions, right?
In this process, they need to do much more than ask a question.
Simply put, if you can't understand the content of the paper, how can you ask questions?
How to judge whether the other party's answer is right or wrong?
Deligne and Faltings said they were going out for a drink, but in fact they just went out for dinner.
By the way, I drank some beer.
During work, it is still very necessary to keep a clear mind.
Those before were just jokes between the two of them.
It's just that Faltins came back with a can and prepared to drink it before going to bed.
In this regard, Deligne could only shake his head helplessly.
Germans are probably the most beer-loving people in the world, right?
After nightfall, time is beating forward with its inherent frequency.
Although some people think it dances too fast, some people think it dances too slow.
But time is equal to everyone.
The speed is only due to the difference in mood.
Looking at Harold Hoofgot outside the window, I felt that the time passed too slowly.
It has been too slow since he uploaded the first draft of the paper to the preprint website e-Print arXiv until now.
He was so eager to prove Goldbach's conjecture, just to put this mathematical problem that has attracted the attention of the world under his own name.
But in the end, he was made to wait for so long.
But fortunately, there will be the final result tomorrow.
Harold Hoofgot had great confidence in his proof process.
He believes that not everyone can catch the flash of inspiration.
Even in the face of Chen Zhou, a new star in mathematics who suddenly appeared, even if Chen Zhou said his proof was the correct way to open it.
Harold Hoofgot wasn't afraid either.
He believed that he seized the opportunity to prove Goldbach's conjecture, not Chen Zhou.
Even at the beginning, he was a little anxious and only wanted to prove the correctness of Goldbach's conjecture.
Thus ignoring some details in the proof.
But after this period of revision, coupled with the feedback from the reviewers.
He felt that there was no problem with his thesis.
At least there are no fatal flaws.
As long as there are no fatal flaws, then the final winner of this report must be him!
Therefore, the closer the time came, the more impatient he became.
After all, the honor that should belong to him has been dragged to the present, which is really impatient.
Looking out of the window again, Harold Hoofgot took a deep breath, closed the window, and drew the curtains.
But, unfortunately, he couldn't fall asleep anyway.
From time to time, he glanced at the time and calculated how long it was before the report meeting began.
Early the next morning, intermittent voices came from the corridor of the hotel.
This is the waiter who got up early to clean up, talking about the report meeting that will start today.
Although the voice seemed abrupt, it was not loud.
Therefore, the two waiters did not expect that someone would open the door of the room and take a look at them.
And this person was none other than Harold Hoofgot who was thinking about the lecture.
According to the process of the report meeting, he and Chen Zhou will give their respective mathematics lectures in sequence according to the order in which the papers are published.
He first, followed by Chen Zhou.
From Harold Hoofgot's point of view, this was an excellent arrangement.
As long as in his lectures no one asks fatal questions.
Then, the uncertainty of the final result is completely eliminated.
Chen Zhou's lectures later will be dispensable.
Therefore, he must seize the opportunity and make a final decision.
So, Harold Hoofgot got up early in the morning, started to check his PPT, sorted out the questions asked by the reviewers, and re-read the content he had sorted out.
After what had happened last night, Harold Hoofgot happened to hear conversation outside.
He thought it was a member of the conference.
So, he went out of the room, ready to go to the venue of this report meeting.
Although Harold Hoofgot got up early, he came early.
However, when he arrived at the venue, there were already many people in the venue.
Everyone was chatting excitedly, discussing the thesis of Harold Hoofgot and Chen Zhou.
After listening for a while, a smile appeared on the corner of Harold Hoofgot's mouth.
Everyone's thoughts are the same.
Because he was the first to publish, he took advantage of the time.
As long as his thesis is not "the wrong way to open it" as Chen Zhou said.
Well, he wins.
As the time gradually approached 9:[-] a.m., more and more people were in the venue.
After Wiles proved Fermat's last theorem, two hundred mathematicians attended the lecture at the Newton Institute of Cambridge University.
Today, the number of mathematicians on site far exceeds two hundred.
Perhaps compared to Wiles' lecture, today's lecture has more sparks of collision, right?
When Chen Zhou came to the venue, Harold Hoofgot had already gone to the backstage and was ready to go.
Therefore, the two did not meet.
Together with Chen Zhou, there are Yang Yiyi, Shen Jing and others.
It was with great difficulty that Shen Jing got a spot with Wu Xiping and came to Princeton.
Therefore, as soon as he saw Chen Zhou yesterday, he immediately said: "Boss, don't let me make this trip for nothing! I can wait to go back and brag with my brothers!"
Chen Zhou just smiled at that time, but didn't say much.
9 am exactly.
This report meeting attracted worldwide attention and was called the "Battle of the Century" by the media and countless netizens.
Officially begin.
On the stage, Harold Hoofgot had opened the PPT and began to talk about his proof process.
Under the stage, the auditorium, which can accommodate thousands of people, is full of seats.
Moreover, there are no less than [-] mathematicians among them!
Among the five hundred mathematicians, there are bigwigs in various fields of mathematics.
There are Qiu Chengtong, Tao Zhexuan, Artin, Faltings, Deligne, Langlands and others that Chen Zhou is fairly familiar with.
There are also winners of the Fields Medal and the Wolf Prize in Mathematics, such as Quillen, Baker, Smail, and Griffith, which Chen Zhou is not familiar with.
At the beginning, Harold Hoofgot was a little nervous when facing so many colleagues in the mathematics field.
But as the lecture continued, he gradually adjusted.
The speed of slide switching, as well as the speed of his speech, have also accelerated a lot.
There were already many people in the audience, and they gradually couldn't keep up with Harold Hoofgot's rhythm.
Even though many people have studied the papers of Harold Hoofgot.
But it was still impossible to keep up with Harold Hoofgot's train of thought.
After all, some content can be understood without preparation.
If you don’t understand, you still don’t understand.
People like Terence Tao, Faltings, etc., also jotted down possible problems during the listening process.
If you get the answer in the following content.
Then they cross it out.
If you don't get an answer, wait for the Q&A session.
As for Chen Zhou, although he also put two pieces of draft paper in front of him.
But until now, I haven't written a word or a symbol.
He was waiting for that long-discovered flaw.
Harold Hoofgot on the stage was completely immersed in his narration.
He has seen the honor after proving Goldbach's conjecture, and is waving to him.
Then he switched to a slide again.
And Chen Zhou, who saw this slide in the audience, narrowed his eyes slightly, picked up a pen and began to write down the problem that had been discovered long ago.
That one fatal flaw!
Harold Hoofgot didn't see this problem.
The content of this part has not been modified at all!
Thank you book friend abigtree2004 for the 100 starting coins!
Thanks to book friend Yan Hongxue for the 100 starting coins!
Thank you book friend Hongchen for the 3687 starting point coins that I traveled alone on 1500!
(End of this chapter)
Princeton is probably best known to the world as Princeton University and the Princeton Institute for Advanced Study.
Because there have been too many scientific masters here.
Including now, here is also the center of mathematics in the world.
Anyone who is a well-known scholar will probably be inextricably linked with this place.
Today's Princeton welcomes many "outsiders" of different skin colors, different countries, and different occupations.
And the reason why everyone came here today is only for one purpose.
That is what will start tomorrow, this world-renowned report meeting.
They are all looking forward to the "wonderful duel" between Chen Zhou and Harold Hoofgot starting tomorrow.
I am also looking forward to the Goldbach conjecture, which originated in 1742, challenged mankind for nearly three centuries, shocked the world many times, exhausted the energy of many of the most outstanding brains of mankind, and also fascinated thousands of amateurs. its end result.
In short, this will definitely be a report meeting destined to be recorded in history in the 21st century.
Although the content of the report meeting starting tomorrow, only a very small number of people can understand it.
But that doesn't stop others from coming here to witness a truly meaningful moment they've been looking forward to.
Take the brother on Chen Zhou's Weibo who said he wanted to broadcast live. What he wanted was to witness this historic moment with his own eyes and record it with his own hands.
At this time, the old man had also arrived in Princeton, and was guarding the entrance of the hotel where the report was held.
For nothing else, he just wanted to cheer Chen Zhou with the blessings of countless netizens.
He hoped that Chen Zhou would leave the right to prove Goldbach's conjecture, which Hua people have been thinking about, in the hands of Hua people.
However, he waited until the sky darkened, but he didn't see Chen Zhou.
He can guarantee that he will never miss or let go of anyone who looks similar to Chen Zhou.
However, Chen Zhou was not seen appearing.
In desperation, he could only return to the hotel where he lived, quietly waiting for the report meeting tomorrow.
In fact, Chen Zhou did pass in front of this old man.
However, Chen Zhou was wearing a hat, and the brim of the hat was pushed down extremely low.
Except for Professor A Ting and others who were with him, no one else knew that the person wearing the hat was Chen Zhou.
Because of this, this old man with good wishes didn't find Chen Zhou.
As for Chen Zhou, since entering the hotel, he has been in the room and never came out.
He is replying to the reviewer's email.
In the email, there are some questions raised about the paper.
Although the report meeting is about to start, the length of the report meeting is considered.
It is impossible to put all the problems in the report meeting.
Therefore, these reviewers sent some questions to Chen Zhou by email.
Chen Zhou was so happy, at least he didn't have to worry about being recognized when he went out.
Then lead to some unnecessary troubles.
In this way, staying in the room, while answering emails, you can also organize your own thoughts.
Find some details that may be overlooked by yourself.
Be fully prepared for the report meeting that starts tomorrow.
Speaking of which, Chen Zhou's paper reviewers are all his "old friends".
Among them, there are three mathematicians, Faltins, Deligne, and Langlands, who are in charge of reviewing his paper on the proof of Kramer's conjecture.
While Chen Zhou was answering the questions in the email, Faltings and the others were also carefully reviewing the paper.
"Deligne, how is the progress on your side?"
Faltings glanced at the person sitting not far away, and gently squeezed the center of his brows.
Deligne, who heard the voice, turned his head and glanced at Faltings, and replied: "My side is going well, and he answered all the questions sent to Chen Zhou. It won't take long. The responsible part should be able to complete the preliminary review."
After a pause, Deligne smiled again and said, "However, I don't think your condition is very good. I think you probably need a bottle of German stout now to refresh yourself."
Faltins let go of the hand pinching his eyebrows, and shook his head helplessly at Deligne: "After all, I am getting older, and my thinking is not as active as when I was young..."
Deligne put away his smile, nodded slightly, and said with emotion: "As we grow older, although we have richer knowledge and experience, we have gradually lost the active thinking that is most needed for mathematical innovation. , we are all old..."
"Mathematics has always been dominated by young people, and the future belongs to these young people." Faltings finished speaking, put down the pen in his hand, gently closed the typed draft of the thesis, got up and said to Deligne, "Go Well, just as you said, let's go drink some beer first, and then come back to continue."
Deligne was stunned for a moment, and then teased: "Aren't you afraid that the brains of the elderly will completely lose their sensitive thinking ability due to alcohol paralysis?"
When Faltings heard the words, he immediately stared and said, "Are you going?"
"Go, go..." Deligne said quickly, "As long as it doesn't affect the normal progress of tomorrow's report meeting..."
Faltings, who was holding his coat, heard the second half of Deligne's words. He glanced sharply at the printed manuscript on the table, and said softly: "I have prepared the questions that should be asked. .”
Deligne raised his head slightly and glanced at the German old man.
Faltings also happened to look up and look at the Belgian Viscount.
The two smiled at each other.
Even though they are really old, these days, they have really worried a lot about the review of Gechai's proof paper.
However, they are extremely serious about Goldbach's conjecture.
This is also the attitude and the most basic respect for a nearly 300-year-old mathematical problem.
In any case, the proof of Goldbach's conjecture wants to be recognized by the entire academic community.
You have to get past them first.
For the report meeting that starts tomorrow, they won't release water.
Like Faltings and Deligne, there are Langlands, Fefferman, Wiles and others.
They also encountered a lot of trouble when reviewing the manuscript.
Just like Wiles' paper proving Fermat's last theorem, for the papers of Chen Zhou and Harold Hoofgot, they also carefully checked every logical link of the part they were responsible for.
If the paper itself cannot be logically self-consistent, then there is no need to continue the review.
But this is an extremely exhausting job.
This kind of consumption is not only reflected in time and details, but also in the content of the paper itself.
The two papers are a melting pot of mathematical tools and ideas such as sieve method, circle method, density ratio method, and distribution deconstruction method.
I want to completely clarify the relationship between these mathematical tools, especially Chen Zhou's distribution deconstruction method, which was born not long ago.
Its difficulty can be imagined.
Although due to the particularity of the paper, the reviewers can throw questions to the contributors at any time in order to get answers.
However, there is always a process of discovering and asking questions, right?
In this process, they need to do much more than ask a question.
Simply put, if you can't understand the content of the paper, how can you ask questions?
How to judge whether the other party's answer is right or wrong?
Deligne and Faltings said they were going out for a drink, but in fact they just went out for dinner.
By the way, I drank some beer.
During work, it is still very necessary to keep a clear mind.
Those before were just jokes between the two of them.
It's just that Faltins came back with a can and prepared to drink it before going to bed.
In this regard, Deligne could only shake his head helplessly.
Germans are probably the most beer-loving people in the world, right?
After nightfall, time is beating forward with its inherent frequency.
Although some people think it dances too fast, some people think it dances too slow.
But time is equal to everyone.
The speed is only due to the difference in mood.
Looking at Harold Hoofgot outside the window, I felt that the time passed too slowly.
It has been too slow since he uploaded the first draft of the paper to the preprint website e-Print arXiv until now.
He was so eager to prove Goldbach's conjecture, just to put this mathematical problem that has attracted the attention of the world under his own name.
But in the end, he was made to wait for so long.
But fortunately, there will be the final result tomorrow.
Harold Hoofgot had great confidence in his proof process.
He believes that not everyone can catch the flash of inspiration.
Even in the face of Chen Zhou, a new star in mathematics who suddenly appeared, even if Chen Zhou said his proof was the correct way to open it.
Harold Hoofgot wasn't afraid either.
He believed that he seized the opportunity to prove Goldbach's conjecture, not Chen Zhou.
Even at the beginning, he was a little anxious and only wanted to prove the correctness of Goldbach's conjecture.
Thus ignoring some details in the proof.
But after this period of revision, coupled with the feedback from the reviewers.
He felt that there was no problem with his thesis.
At least there are no fatal flaws.
As long as there are no fatal flaws, then the final winner of this report must be him!
Therefore, the closer the time came, the more impatient he became.
After all, the honor that should belong to him has been dragged to the present, which is really impatient.
Looking out of the window again, Harold Hoofgot took a deep breath, closed the window, and drew the curtains.
But, unfortunately, he couldn't fall asleep anyway.
From time to time, he glanced at the time and calculated how long it was before the report meeting began.
Early the next morning, intermittent voices came from the corridor of the hotel.
This is the waiter who got up early to clean up, talking about the report meeting that will start today.
Although the voice seemed abrupt, it was not loud.
Therefore, the two waiters did not expect that someone would open the door of the room and take a look at them.
And this person was none other than Harold Hoofgot who was thinking about the lecture.
According to the process of the report meeting, he and Chen Zhou will give their respective mathematics lectures in sequence according to the order in which the papers are published.
He first, followed by Chen Zhou.
From Harold Hoofgot's point of view, this was an excellent arrangement.
As long as in his lectures no one asks fatal questions.
Then, the uncertainty of the final result is completely eliminated.
Chen Zhou's lectures later will be dispensable.
Therefore, he must seize the opportunity and make a final decision.
So, Harold Hoofgot got up early in the morning, started to check his PPT, sorted out the questions asked by the reviewers, and re-read the content he had sorted out.
After what had happened last night, Harold Hoofgot happened to hear conversation outside.
He thought it was a member of the conference.
So, he went out of the room, ready to go to the venue of this report meeting.
Although Harold Hoofgot got up early, he came early.
However, when he arrived at the venue, there were already many people in the venue.
Everyone was chatting excitedly, discussing the thesis of Harold Hoofgot and Chen Zhou.
After listening for a while, a smile appeared on the corner of Harold Hoofgot's mouth.
Everyone's thoughts are the same.
Because he was the first to publish, he took advantage of the time.
As long as his thesis is not "the wrong way to open it" as Chen Zhou said.
Well, he wins.
As the time gradually approached 9:[-] a.m., more and more people were in the venue.
After Wiles proved Fermat's last theorem, two hundred mathematicians attended the lecture at the Newton Institute of Cambridge University.
Today, the number of mathematicians on site far exceeds two hundred.
Perhaps compared to Wiles' lecture, today's lecture has more sparks of collision, right?
When Chen Zhou came to the venue, Harold Hoofgot had already gone to the backstage and was ready to go.
Therefore, the two did not meet.
Together with Chen Zhou, there are Yang Yiyi, Shen Jing and others.
It was with great difficulty that Shen Jing got a spot with Wu Xiping and came to Princeton.
Therefore, as soon as he saw Chen Zhou yesterday, he immediately said: "Boss, don't let me make this trip for nothing! I can wait to go back and brag with my brothers!"
Chen Zhou just smiled at that time, but didn't say much.
9 am exactly.
This report meeting attracted worldwide attention and was called the "Battle of the Century" by the media and countless netizens.
Officially begin.
On the stage, Harold Hoofgot had opened the PPT and began to talk about his proof process.
Under the stage, the auditorium, which can accommodate thousands of people, is full of seats.
Moreover, there are no less than [-] mathematicians among them!
Among the five hundred mathematicians, there are bigwigs in various fields of mathematics.
There are Qiu Chengtong, Tao Zhexuan, Artin, Faltings, Deligne, Langlands and others that Chen Zhou is fairly familiar with.
There are also winners of the Fields Medal and the Wolf Prize in Mathematics, such as Quillen, Baker, Smail, and Griffith, which Chen Zhou is not familiar with.
At the beginning, Harold Hoofgot was a little nervous when facing so many colleagues in the mathematics field.
But as the lecture continued, he gradually adjusted.
The speed of slide switching, as well as the speed of his speech, have also accelerated a lot.
There were already many people in the audience, and they gradually couldn't keep up with Harold Hoofgot's rhythm.
Even though many people have studied the papers of Harold Hoofgot.
But it was still impossible to keep up with Harold Hoofgot's train of thought.
After all, some content can be understood without preparation.
If you don’t understand, you still don’t understand.
People like Terence Tao, Faltings, etc., also jotted down possible problems during the listening process.
If you get the answer in the following content.
Then they cross it out.
If you don't get an answer, wait for the Q&A session.
As for Chen Zhou, although he also put two pieces of draft paper in front of him.
But until now, I haven't written a word or a symbol.
He was waiting for that long-discovered flaw.
Harold Hoofgot on the stage was completely immersed in his narration.
He has seen the honor after proving Goldbach's conjecture, and is waving to him.
Then he switched to a slide again.
And Chen Zhou, who saw this slide in the audience, narrowed his eyes slightly, picked up a pen and began to write down the problem that had been discovered long ago.
That one fatal flaw!
Harold Hoofgot didn't see this problem.
The content of this part has not been modified at all!
Thank you book friend abigtree2004 for the 100 starting coins!
Thanks to book friend Yan Hongxue for the 100 starting coins!
Thank you book friend Hongchen for the 3687 starting point coins that I traveled alone on 1500!
(End of this chapter)
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