Chapter 104 (2/2)
This question It's simple? Has the final say,
, you are the curve wrecker.
The whole class rolled their eyes.
Cheng Nuo shrugged and continued to preach. ”Before I talk about this problem, I'd like to tell you a model called Rubik's cube matrix!”
Why can Cheng Nuo know the Rubik's cube matrix?
Normally speaking, senior high school will not involve this kind of knowledge.
But who is Cheng Nuo? He's a bully!
One of the characteristics of Xueba is that you will never be satisfied with learning only the knowledge in class!
Do you remember the pile of books about the world's mathematical problems that Cheng bought back from the bookstore? The Rubik's cube matrix is used in the reasoning process of one of the problems. Cheng Nuo wrote it down by the way.
Cheng Nuo stood on the podium, will Rubik's cube matrix of the three solutions are told once.
”After listening to this theorem, do you think the problem is much simpler. First of all, the number in the middle of the first line must be 1, the position of number 2... ”Under the platform, the students were dizzy and confused. Cheng Nuo talked on the platform with relish.
”Well, that's all I want to say. Thank you very much.” With that, Cheng Nuo stepped down from the platform.
Pa Pa ~ ~
the whole class applauded subconsciously.
After Cheng Nuo stepped off the platform, Comrade Tang stood in front of the desk with an embarrassed face.
Girl! Finish what I want to say. What can I say?!
Mr. Tang's thinking matrix was introduced to the students before the college entrance examination.
But now
Er Well, Cheng Nuo told me more about the Rubik's cube matrix than I did, so I'm not going to make a fool of myself as a teacher.
”All right. Let's take out the set of questions in the paper Old Tang coughed awkwardly for a while, and did not ask the students if they understood. He quickly changed the topic.
”Wow, Muleng, Cheng Nuo is really good. Such questions can be used! ” Sue's little bright eyes were full of little stars.
Mu Leng's mouth rose slightly, ”this is the The rebellious one
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”Well, class is over. Mullen and Chenault, you two come to the office with me
With the bell ringing, old Tang just finished the last question.
Cheng Nuo and Mu Leng look at each other. They are all in a fog. They don't know what Lao Tang is looking for, but they still follow him to the office.
When he went down the stairs, Cheng Nuo got close to Mu Leng and whispered in a slightly worried voice, ”sister Leng, do you think that we two fell in love with each other by the old Tang?”
Mu Leng glanced at Cheng Nuo lightly and said, ”you say it!”
Cheng Nuo shrunk his neck, a face chat up, ”joking, joking.”
”But, sister Leng, do you really stop thinking about us? You see, you are Xueba, and I am Xueba. Xueba is matched with Xueba. We can be said to be in a good match. The children born must be Xueba! ” Cheng Nuo clenched his fists and said.
Mu Leng pursed her lips and said ambiguously, ”after the college entrance examination, we are talking about this problem.”
”OK, I'll wait for you.” Cheng Nuo smiles faintly.
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Note 1: the algorithm of the other two cases of magic square matrix. (the number of words in the text has reached 2000, which is not the number of water words. This is to help you learn this problem!! Please understand the author's good intentions.)
(2) When n is a multiple of 4, the symmetry element exchange method is used.
Firstly, the numbers from 1 to n × n are filled in the matrix from top to bottom and from left to right in order
then the numbers on the two diagonals of all 4 × 4 sub matrices of the square matrix are symmetrically exchanged with respect to the center of the square matrix (note that the number above the diagonal of each sub matrix) is exchanged, that is, a (I, J) is exchanged with a (n + 1-I, N + 1-J), and the numbers at all other positions remain unchanged. (3) when n is any other even number
when n is an even number (i.e. 4N + 2 shape), the large square matrix is first decomposed into four odd (2m + 1 order) submatrix.
According to the odd order Rubik's cube of odd order, the corresponding values of the four sub matrices are assigned
the upper left subarray is the smallest (I), the lower right subarray is the second smaller (I + V), the lower left subarray is the largest (I + 3V), and the upper right subarray is the second largest (I + 2V)
that is, the difference of the corresponding elements of the four subarrays is V, where V = n * N4
the arrangement of the four sub matrices from small to large is ① ③ ④ ②
and then the corresponding element exchange is made: a (I, J) Do the corresponding exchange with a (I + U, J) in the same column (J & & T-1 or J & & amp; N-t + 1),
note that J can go to zero.
A (t-1, 0) and a (T + U-1, 0); a (t-1, t-1) and a (T + U-1, t-1) exchange
where u = N2, t = (n + 2) 4. The above exchange makes the sum of elements in each row and column equal to the sum of the elements on the two diagonals.
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PS: I have detailed the steps to this extent. If you don't I can't help it.