Magus Tech (Technological Wizard)

"What do you think?" The great scholar Suratis asked Li Cha, looking at him.

Richard took his eyes away from the title of the papyrus scroll, and his eyes flashed: "22 days."

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

"If you use a suitable method to answer this question - let the fake university scholar Su La find the thief Raddy hiding in the secret room, it will take up to 22 days." Richard said.

Surati looked at Li Cha for a few seconds, then pondered, and nodded in appreciation for a moment: "Well, yes, it is very consistent with my previous guess, yes, it is 22 God. Come on boy, tell me your thoughts, and let me see if you have anything different from mine or something wrong."

"Think of it this way and number all thirteen houses - from 1 to 13. Then in the question, the thief Raddy changes rooms, or even to odd - such as from 1 to 2 room, or from odd to even - say, from room 1 to room 2.

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

If the thief Raddy is in an 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 search room 12 on the eleventh day So far, the thief Lucky will be very likely to be searched in the process. Because the distance between the fake university scholar Sula who searches the room and the thief Raddy 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 Raddy is caught.

And if the search does not find the thief in the end, it means that the thief Raddy stayed in the odd-numbered room on the first day. Then on the first day, the twelfth day, he will definitely stay in the even-numbered room. In this way, the fake university scholar Sula can go back and continue to search from room 2, then the worst case is to catch the thief Raddy in room 12 on the 22nd day and get back the stolen treasure . "

"Well..." After listening to Li Cha's words, the great scholar Suratis pondered for a long time, then looked at Li Cha and nodded, "Well, yes, your thinking is very correct, and it is almost exactly the same as mine. You... Well, wait a moment, I will write a draft of the reply letter to that old bastard of Nayadod."

After speaking, the great scholar Surates picked up the quill, opened a new papyrus scroll, and began to write "swipe".

After a while, the writing is almost finished, Suratis looked at the content, fell into deep thought again, and said to Richard: "Adotus deliberately made problems to embarrass me, although...cough, although it didn't really embarrass me, but I should also answer him with a similar problem.

I've thought of several problems, but none of them are quite right. Then do you have any suitable questions, preferably the ones that are very difficult to answer..."

"Uh..." Li Cha's eyes flashed, and his thoughts flew.

A very difficult problem to solve? There are too many, and what he has always wanted to know is one of them - what is the truth of this world, what is the essence of transmigration?

In addition, several problems that caused the book spirit to not respond to the test of the book spirit a long time ago can also be considered - the grand unified theory, the Riemann conjecture, and the accurate value of pi.

However, considering these questions, he also couldn't give an answer, so it would be better to replace it with a few simpler ones. For example... the Poincaré conjecture, which is one of the seven major mathematical problems in the modern earth world, and the Riemann conjecture, has been successfully solved:

Any simply connected, closed three-dimensional manifold is homeomorphic to a three-dimensional sphere.

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

To put it simply, if a rubber band is attached to the surface of an apple, try to stretch it, neither tear it off nor let it leave the surface, so that it can slowly move and contract to a point; Appropriately tied to the surface of a tire,

There is no way to shrink the rubber band to a point without leaving the surface without pulling the rubber band. So the apple surface is "singly connected", the tire surface is not.

Richard was about to speak, but the words stopped, because he suddenly thought of something about topology, which might be a little too challenging to the thinking of the great scholar Suratices in front of him. If he really said it, he would probably need to popularize the definitions of three-dimensional, manifold, and embryo first.

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

So……

"You can think of it this way." Li Cha looked at Suratis and said, "In the numbers, there is a relatively special existence, such as 121, 363, etc. They read from left to right, and they read from right to left, it is the same , this kind of number can be called palindrome. And these numbers are not unfounded, it can be split into many other numbers.

For example, adding the number 56 to its inverse number, 65, yields the palindrome number 121.

For another example, use the number 57 and add it to its reverse number, 75, to get 132. 132 is not a palindrome, but if you add it to its reverse number, 231, you get 363. This palindrome number.

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 - another palindrome after three iterations.

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 many iterations. For example, 89 needs 24 iterations to get the 13-digit palindrome number of 8, 813, 200, 023, and 188.

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

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

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

"..." The great scholar Suratis was silent for a long time. After looking at Li Cha, he silently walked to the side of the desk, took a sip of the cold tea he had brewed at some point in time.

After drinking tea, the great scholar Suratis looked at Richard, and nodded first, expressing his approval: "Well, that's a good question."

Then came two questions—two serious questions.