As we all know, magic is such a digital game. after entering the number of N ^ 2 from 1 to n ^ 2 into the square matrix of N x n, the sum of numbers on each row, column, and diagonal line is the same. As an old Mathematical game, the magic has a strong vitality. Until now, mathematicians are still searching for magic ways that satisfy various strange properties. What's more interesting is that this magical digital matrix has developed into a text game. People found that they entered the following letters in the 4× 4 square matrix. Each column in each row is a word:
C A R D
A R E
R E A R
D A R T
Such a square matrix is called word square ).
Recently I was particularly interested in text games. I began to think about the question: is it possible to enter Chinese characters in the square matrix so that each column of each line is a word? Looking at the Chinese piphilology dictionary on the desktop of my computer, I felt itchy again. So I spent an afternoon searching for Chinese Character magic by using Mathematica. I will share with you the results below.
Because there are many four-character Chinese characters, my main focus is on searching for Level 4 Chinese characters. It is estimated that it is much easier to construct a Chinese character Magic Square than to construct an English magic square-thanks to the unique overlapping words in Chinese. Just find a pair of words like AABB and bbcc, and we get a level 4 magic. For example:
In a hurry
In a hurry
Busy
Busy
This simple magic is unlikely to be implemented in other languages. As you can imagine, there are still many such level 4 magic parties. According to my dictionary, the computer found 13 words in the form of (AABB, bbcc). They are:
Busy, busy
Busy and busy
Safe and secure
Security and stability
Honest, real
Practically, practically
It's actually true.
Solid, real
Strictly and practically
Solid, real
Cold, clear, and clear
Happy and painful
Warehouse, conscientious
It can be seen that there are at least 13 Chinese Characters in Level 4.
However, most readers will think that this magic is too "ordinary. Is there any other level 4 Chinese Character Magic Square? Yes. The computer provides the following solutions when looking for the magic square of Chinese Characters in other shapes:
Optional
Title and privilege
Optional
No power, no power
This increases the number of original two words actually contained in the magic to three. However, the results seem to be still not perfect. I hope that the four Chinese characters are different from each other. Does this perfect Level 4 magic exist? On the one hand, because the number of words containing a specific Chinese character is very limited, it is much more difficult to construct a perfect Chinese Character Magic Square than to construct an English magic square. On the other hand, when Chinese words are created, the association between the phoneme and the semantics provides favorable conditions for the existence of Chinese characters. If we can find a semantic circle, the words in this circle are always those words, and there is a magic between them. Fortunately, such a semantic circle exists-the computer has found such a group of familiar words that show Chinese language characteristics, forming a Chinese character magic:
Entire party and whole country
Party and country
National People's Congress
National events
However, the above magic shows that the first word uses the same word. Can I avoid having different words in the same word? Yes. The computer gives the perfect Level 4 Chinese Character magic square below.
Western European countries
European countries
People of all countries
National Civil Affairs Commission
This level-4 magic is quite rare to satisfy words that are not repeated and have no duplicates in each word. In my dictionary, the level 4 magic is the only solution.
Some readers may not be satisfied: the above slides depend on symmetry. Is it possible to create an asymmetric text Phantom? In other words, can n horizontal words and n vertical words be different? In English text games, this is called "double word square ). People have discovered many double-character magic ways, such:
L A C K
I r o n
M e r e
B A K E
In Chinese, there is too much hope for a level-4 dual-text magic, but the level-3 Dual-text magic may exist. In fact, because English is a pinyin text with only 26 letters, and thousands of commonly used Chinese characters, we may be able to do something that is beyond our reach: not only are 2n words different from each other, but n ^ 2 words in the grid are different. Unfortunately, the computer did not find such a perfect pair of Chinese characters. The two closest results are as follows:
There are only three-level dual-Chinese characters with two duplicate words:
Shandong
Northwest China
Provincial/ministerial level
There is only one level 3 Dual Chinese Character Magic Square for repeated words:
China News Service
Student Union
Life
Because most Chinese words are double words, it is much easier to create two-level dual-Chinese characters. By taking advantage of the word-building characteristics of Chinese Double-character pairs, we can not only ensure that the four characters in the second-order double-character Magic Square are different, but also ensure that the two diagonal lines of the square matrix are just words. For example:
Heaven
Underground
The search results in this afternoon are a bit blank in the Chinese text game, but the exploration of text magic is far from over. If we expand the dictionary, or add phrases or even sentences, can we construct a text Magic Square with a higher order? The omnipotent netizens continue to work hard.