Magus Tech Chapter 283: The Poincaré conjecture and the Lychrell number

"What do you think?" The great scholar Sura Di looked at Richard and asked.

Li Cha looked away from the title of the papyrus scroll, his eyes flickered and said: "22 days."

"Huh?" The great scholar Surat was stunned, "What 22 days?"

"If you use a suitable method to solve this question—it will take up to 22 days for the fake university student Sura to find the thief Ladi hiding in the secret room." Richard said.

Suradi looked at Li Cha for a few seconds, then pondered, and then nodded appreciatively for a moment: "Well, yes, it is very consistent with my previous guess, yes , That’s 22 days. Come on kid, tell me about your thinking, and let me see if you have anything different or wrong from me.”

"You can think about the problem in this way, number all thirteen houses-from No. 1 to No. 13. Then in the title, the thief Lardy changes rooms, either from even numbers to odd numbers-for example, from room No. 1 To get to room 2, either change from an odd number to an even number—for example, from room 1 to room 2.

In this way, we make two assumptions: on the first day, the thief Ruddy is in the even-numbered room; or, on the first day, the thief Ruddy is in the odd-numbered room.

If the thief Lardy is in the even-numbered room on the first day, then we search room 2 on the first day, room 3 on the second day, room 4 on the third day, and so on until the eleventh day As far as room 12, the thief Larch is very likely to be searched in the process. Because the distance between the fake university scholar Sura who searched the room and the thief Ladi will definitely be an even number—either 0 or a multiple of 2. When the distance is 0, it means the search is successful and the thief Lady is caught.

And if this search does not find the thief in the end, then it means that the thief Lardy stayed in the odd-numbered room on the first day. Then on the next day—the twelfth day, he will definitely stay in the even-numbered room. In this way, the fake university student Sura can go back and continue searching from Room 2. In the worst case, the thief Ladi will be caught in Room 12 on the 22nd day and the stolen treasure will be taken back. . "

"Well..." After listening to Li Cha's words, the great scholar Suradi pondered for a long time, then looked at Li Cha and nodded, "Well, yes, your thinking is very correct, almost exactly the same as mine. You...well, wait a minute, I will write a draft of the reply to that old **** Naya Dodd."

After finishing speaking, the great scholar Su Ladi picked up the quill pen, opened a new papyrus scroll, and began to "scrape and swipe" to write.

A long time later, the writing was almost done. Surati looked at the content, fell into deep thought again, and said to Richard: "Yadod deliberately made things difficult for me, although... cough, although it didn't make me really It's difficult, but I should answer him with a similar problem.

I have thought of several problems, but none of them are suitable. Then do you have a suitable question, preferably one that is very difficult to answer..."

"Eh..." Li Cha's eyes flickered and his thoughts raced.

Extremely difficult puzzle to solve? There were too many, and what he always wanted to know was one of them - what is the truth of this world, what is the essence of time travel?

In addition, the test of Shuling a long time ago, which has caused Shuling to not respond to a few questions, can also be considered-the grand unified theory, the Riemann conjecture, and the exact value of pi.

However, considering these questions, he was also unable to give an answer, and it would be better to switch to a few simpler ones. For example... the Poincaré conjecture, which belongs to one of the seven major mathematical problems in the modern earth world, but has been successfully solved, like the Riemann conjecture:

Any simply connected, closed 3D manifold is homeomorphic to a 3D spherical surface.

Simply speaking, every closed three-dimensional object without holes is topologically equivalent to a three-dimensional sphere.

To put it simply, if there is a rubber band tied to the surface of an apple, try to stretch it, neither tear it off nor let it leave the surface, you can let it move slowly and shrink to a point; but put this The rubber band is bound to the surface of a tire in a proper way, and there is no way to shrink the rubber band to a point without pulling the rubber band off the surface. Thus, while the surface of an apple is "simply connected", the surface of a tire is not.

Li Cha was about to speak out, but the words stopped when he reached his mouth, because he suddenly thought of something about topology, which might be a bit too challenging to the thinking of the great scholar Surat in front of him. If he really said it, he probably needs to popularize the definitions of three-dimensional, manifold, and embryo first.

So... let's change to a simpler one, preferably a purely numerical problem-a "strength problem" that has no technical content but requires a lot of calculations to complete.

Then...

"You can think of it this way." Li Cha looked at Su Ladi and said, "There is a special kind of existence in numbers, such as 121, 363, etc. They read from left to right, and from right to left, It is the same, this kind of numbers can be called palindromic numbers. And these numbers are not groundless, they can be split into many other numbers.

For example, if you add the number 56 to its reverse number, 65, you can get the palindrome number 121.

For another example, take the number 57 and add it to its reverse number - 75, and you get 132. 132 is not a palindromic number ~IndoMTL.com~ but add it to its reverse number - 231 to continue Adding up, you get the palindrome number 363.

For example, add 95 to the number 59 to get 154. Add 451 to 154 to get 605. Add 506 to 605 to get 1111—after three iterations, it is another palindrome.

In fact, about 90% of the numbers within 100 can get a palindrome within seven iterations, and about 80% can get a palindrome within four iterations.

Of course, there are also more iterations. For example, 89 needs 24 iterations to get the 13-digit palindrome number of 8, 813, 200, 023, and 188.

After exceeding 100, such as the number 10,911, it takes 55 iterations to get a 28-digit palindrome number—4,668,731,596,684,224,866,951,378,664.

Super large numbers like 1, 186, 060, 307, 891, 929, 990 need 261 iterations to get a qualified palindrome number, and the result has exceeded 100 digits, reaching 119 bits.

So is there such a number, no matter how many iterations it goes through, it can't get a palindromic number? We can call it the Lychrell number, if it exists, what is the smallest? "

"..." The great scholar Surat was silent for a long time. He looked at Li Cha, walked to the side of the desk silently, took a sip of the cold tea that he brewed at some time.

After drinking the tea, the great scholar Suradi looked at Li Cha, nodded his head in agreement, and said, "Well, it's a good topic."

Then ask two questions—two very serious questions.