Magus Tech

"What do you think?" University scholar Suradi asked Richard.

Richard’s eyes retreated from the title of the papyrus scroll, and his eyes flashed: "22 days."

"Huh?" Sorad, a college student, "What 22 days?"

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

Suradi looked at Richard for a few seconds, and then pondered, for a moment, he nodded appreciatively: "Well, yes, it is very consistent with my previous guess, yes, it is 22 God. Come on kid, tell me your thoughts, let me see if you have anything different and wrong."

"You can think about it this way and number all the 13 houses-from 1 to 13. Then in the title, the thief Ladi changed the room, or even to odd-for example, from room 2 to 1 The rooms are either changed from odd to even-for example from room 1 to room 2.

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

If the thief Ladi was in the even room on the first day, then we searched room 2 on the first day, room 3 on the second day, room 4 on the third day, and room 12 on the 11th day. So far, the thief Raki will be very likely to be searched in this process.Because the distance between the fake college student Sula who searches 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 that the search is successful and the thief Ladi is caught.

And if you search like this, and there is no thief in the end, it means that the thief Ladi stayed in the odd room on the first day.Then on the first day-the twelfth day, he will definitely stay in the even room.In this way, the fake university student Sula can go back and continue searching from room 2. Then the worst case is to catch the thief Ladi in room 12 on the 22nd day and take back the stolen baby. ."

"Well..." University scholar Soradi pondered for a long time after listening to Richard, then looked at Richard and nodded, "Well, yes, your idea is very correct, almost the same as mine. You... Uh, wait a minute, I’ll write a draft of the letter to the old bastard of Nayadod."

After finishing speaking, the university student Suradi took the quill, opened a new papyrus scroll, and began to "swipe".

Halfway through, the writing was almost finished, and Soratie looked at the content and fell into contemplation. He said to Richard: "Adold deliberately made a problem that embarrassed me, although...cough, although it didn't really embarrass me, but I should respond to him with a similar problem.

I have thought of several problems, but they are not very suitable.Do you have any suitable questions? The best ones are very difficult to answer..."

"Ah..." Li Cha's eyes flickered and his thoughts flew.

Very difficult to solve?That's too much, and he always wanted to know one of them-what is the truth of this world and what is the essence of traversing?

In addition to this, a long time ago, the "Spirit of Monroe" was tested by Shuling, which caused several problems that Shuling has not responded to so far. It can also be counted - Grand Unified Theory, Riemann Conjecture, and the exact value of pi.

However, considering these questions, he was also unable to give the answer, and it was better to compare a few simple points.For example... The Poincaré conjecture, which is one of the seven major mathematical problems in the modern earth world and has been successfully solved, is the same as the Riemann conjecture:

Any single connected, closed three-dimensional manifold is homeomorphic to a three-dimensional spherical surface.

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

To put it simply, if an apple (or other spherical fruit) is bound with a rubber band on the surface, try to stretch it, neither tear it nor let it leave the surface, you can let it slowly move and shrink to a point; But this rubber band is tied to the surface of a tire in an appropriate way. Without pulling the rubber band, there is no way to shrink the rubber band without leaving the surface and shrinking to a little.Therefore, the apple surface is "single connected", but the tire surface is not.

Richard was about to speak out, but he stopped talking, because he suddenly thought about topology, which might be a bit too much to challenge the thinking of the university student Surahadi.If he really says it, he probably needs to popularize the definition of three-dimensional, manifold and embryo first.

So... let's change to a simpler one, preferably a purely digital problem-a "power problem" that requires little calculation but requires a lot of calculation.

Then...

"Think of it like this." Richard looked at Suradia and said, "There is a special kind of existence in the numbers, such as 121,363, etc. They read from left to right, and read from right to left. This kind of number can be called a palindrome. These numbers are not unfounded, they can be split into many other numbers.

For example, using the number 56 and adding it to his reverse number, 65, you can get the palindrome number 121.

As another example, using the number 57 and adding his reverse order number-75, you get 132. 132 is not a palindrome number, but if you continue to add it and its other reverse order number-231, you get 363. The number of palindromes.

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

In fact, about 100% 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 many iterations. For example, 89 requires 24 iterations to get the 13, palindrome of 8,813,200,023,188.

After more than 100, such as 10,911, it takes 55 iterations to get 28 palindromes-4,668,731,596,684,224,866,951,378,664.

Super large numbers like 1,186,060,307,891,929,990 require 261 iterations to get a qualified palindrome. The result has exceeded 100 digits and reached 119 digits.

So there is no such number, no matter how many iterations it can't get a palindrome number?We can call it the Leclerc number, and if it does exist, what is the minimum?"

"..." The university scholar Suradi was silent. After a long silence, he looked at Richard and walked silently to the side of the desk. He picked up a cup of tea that had been brewed for some time and had been cold. He took a sip.

After drinking the tea, the college student Suradi looked at Richard and first nodded his head, expressing his agreement: "Well, it's a very good topic."

Then ask two questions-two very serious questions.