JP3095973U - Magic square creation game board - Google Patents

Abstract

(57) [Summary] [Problem] An object of the present invention is to provide a magic square creation game board that can easily create a magic square. Kind Code: A1 A magic square for forming a magic square arranged such that the sum of natural numbered vertical, horizontal, and diagonal columns to be put into each square of a 4 × 4 or 5 × 5 square A is equal. In the square creation game board, after subtracting 1 from each of the natural numbers put in the 4 × 4 or 5 × 5 grid A to obtain an integer, the integer is converted to a quaternary or quinary number, and then 4 or 4 A first classification is performed for each number in the 4th or 5th place in quinary, and
After performing the second classification for each number of ones in the quaternary or quinary, the first classification and the second classification are combined to form the identification mark M corresponding to each of the quaternary or quinary And the identification marks M are made to correspond to natural numbers in advance, and are arranged based on a predetermined rule so that a magic square of 4 × 4 or 5 × 5 can be obtained. I have.

Description

[Detailed description of the device]

[0001]

[Technical field to which the device belongs]

  The present invention is a magic square creation game board that can relatively easily create magic squares. Regarding

[0002]

[Prior art]

  As is well known, the array of various numbers called the magic square is known. In particular, arrange each natural number (1, 2, 3, ...) Into each grid of n × n grids. , Vertical, horizontal, and diagonal in the n × n grid in which the natural numbers (1, 2, 3, ...) Are arranged. It is widely known that the magic squares arranged so that the sum of each column (diagonal line) is equal Has been. Generally, 3 × 3, 4 × 4,5 and 5 × 5 cells are widely known. .

[0003]   The magic square is arranged with natural numbers (1, 2, 3, ..., N × n). Regularity that the sum of vertical, horizontal, and diagonal (diagonal) columns in an n × n grid is equal However, it has the feature that there are many array patterns, Use the features of to let children and students experience the mystery and fun of numbers, Attempts have been made to keep the interest in.

[0004]   Moreover, the above magic square has many regular arrangements, but many arrays exist. It also has a variety of features, which is useful for intellectual education to improve the knowledge and intelligence of children and students. It seems that.

[0005]

[Problems to be solved by the device]

  As mentioned above, the magic square creates a mystery and fun of numbers for children and students. Can be tested and provide an opportunity for interest in mathematics and mathematics At the same time, it seems that it is also suitable for intellectual training to enhance knowledge and intelligence. However, each natural number (1, 2, 3, ...) Is put in each grid of n × n grids. , Vertical, horizontal, diagonal (diagonal) columns are arranged so that their sums are equal to create a magic square It's a fairly difficult task to do, and to create a magic square Because time is required, children and students give up creating magic squares, I am tired of creating magic squares and lose interest in magic squares. In a school class where you are feeling sick and have a limited amount of time, you only need to create a magic square. Because the working time is consumed, it is not possible to efficiently teach classes using the magic square there were. In addition, in an attempt to complete the magic square with this device, Fosters logicality as well as enhances the ability of students to sort and reason, which is currently prone to loss. The purpose is also to remove.

[0006]   Therefore, the present invention solves the above problems and facilitates the creation of magic squares. It is possible for children and students to experience the mystery and fun of numbers through the magic square. You can keep your interest in mathematics and mathematics at the same time as you use the magic square The purpose is to provide the means to efficiently carry out the lessons that were held.

[0007]

[Means for solving the problem]

  In order to achieve the above object, the present invention has the following technical means.   That is, each number of natural number N (natural number from 1 to 16) corresponds to each cell of 4 × 4 grid A. Natural numbers N (1,2) are arranged one by one, and are arranged in the 4 × 4 grid A. , 3, 16) are arranged so that the sums of the vertical, horizontal, and diagonal columns are all equal. In the magic square creation game board that creates the magic square,   The above magic square making game board is put in the 4 × 4 grid A that composes the 4 × 4 magic square. Subtracted 1 from each natural number N (1, 2, 3, ... 16) , ... 15), then the above integer (0, 1, 2, ... 15) is converted to a quaternary number. , And further, the first classification is made for each of the fours digit (0, 1, 2, 3) in the above quaternary number. While performing, the second classification is performed for each ones digit (0, 1, 2, 3) in the quaternary number. After that, a first classification is made for each four-digit number (0, 1, 2, 3) in the above quaternary number, and Combine the second classification for each ones digit (0, 1, 2, 3) in quaternary. The identification mark M corresponding to each of the quaternary numbers is formed by and, and A natural number N (1, 2, 3, ... 16) is previously associated with the identification mark M, and The same classification as the first classification in the identification mark M is vertical, horizontal, or diagonal (diagonal). It is not arranged in each row, and the same classification of the second classification in the identification mark M Are arranged so that they do not line up in vertical, horizontal, and diagonal (diagonal) columns. It is configured to get a magic square of × 4, and the above magic square making game board is Game board body with 4 × 4 grid A and 4 × with game board body The identification mark M is attached to the front side C and the natural number N is attached to the back side D arranged on the square A. This is a magic square making game board characterized by being composed of a frame B.

[0008]   Also, each natural number N (natural number from 1 to 25) is equal to each 5 × 5 square in each grid A. Natural numbers N (1,2,2) are arranged one by one and are arranged in the above-mentioned 5 × 5 grid A. 3, ... 25) are arranged so that the sums of the vertical, horizontal, and diagonal columns are all equal. In the magic square creation game board that creates squares,   The above magic square making game board is put in the 5 × 5 grid A that composes the 5 × 5 magic square. Subtracted 1 from each natural number N (1, 2, 3, ... 25) , ... 24) is obtained, and then the above integer (0, 1, 2, ... 24) is converted into a quinary number. , And the first minute for each quintile (0, 1, 2, 3, 4) in the above-mentioned quinary number. Class and the second digit for each ones digit (0, 1, 2, 3, 4) in the quinary number. After performing the classification, the 5th digit (0, 1, 2, 3, 4) 1 classification and 2nd classification for each digit (0, 1, 2, 3, 4) in the quinary number By forming the identification mark M corresponding to each of the five-ary numbers. In addition, a natural number N (1, 2, 3, ... 25) is previously associated with the identification mark M. In addition, the same classification of the first classification in the identification mark M is vertical, horizontal, It is not arranged in each diagonal (diagonal line) row, and the second mark in the identification mark M Arrange so that the same categories of are not aligned in vertical, horizontal, and diagonal (diagonal) columns. By doing so, it is configured so that a 5 × 5 magic square can be obtained. The created game board is a game board body in which a 5 × 5 grid A is described and the game board body described above. The identification mark M on the front side C and the back side D arranged on the 5 × 5 grid A described in A magic square making game board characterized by comprising a frame B with a natural number N attached to It

[0009]   The present invention comprises the above technical means, and the magic square making game board is 4 × 4 or 5 ×. Natural number N (1 that can be put into each grid of grid A of 4x4 or 5x5 in the magic square of 5 , 2, 3, ... 16 or 1, 2, 3, ... , The number of the 4th or 5th place in the above 4 or 5 base number (0, 1, 2, 3 or 0, 1, The first classification performed every 2, 3, 4) and the number of ones digit (0 , 1, 2, 3, or 0, 1, 2, 3, 4) for each second classification Corresponding to a natural number N (1, 2, 3, ... 16 or 1, 2, 3, ... 25) Identification mark M is formed on the grid A of 4 × 4 or 5 × 5. The same classification of the first classification in the separate mark M is displayed in each of vertical, horizontal, and diagonal (diagonal) columns. The same classification of the second classification in the identification mark M is , 4 × 4 or by arranging them so that they do not line up in each row of horizontal and diagonal (diagonal lines) Is configured to obtain a 5x5 magic square, creating a 4x4 or 5x5 magic square Can be done without calculating the sum of the vertical, horizontal, and diagonal (diagonal) columns. Thus, children and students can easily create a magic square.

[0010]   Then, as described above, the magic square creation game board of the present invention can be used to create the magic square. By becoming easier, it is possible to increase the interest of children and students in the magic square. So, through the mystery and fun of the magic square, keep your interest in mathematics and mathematics await In addition to being able to do, it is also useful for intellectual education to improve the knowledge and intelligence of children and students. Of.

[0011]   Furthermore, the magic square creation game board makes it easier to create magic squares. , You can effectively use the lesson time, and you can efficiently conduct lessons using magic squares. .

[0012]

[Embodiment of device]

  Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.   The magic square creation game board of the present invention is a natural number (1, 2, 3, ... 16 or 1,2,3 ... 25) is the sum of the columns in the vertical, horizontal and diagonal (diagonal) lines, etc. It makes it easy to create magic squares that are arranged so that Create magic square without calculating sum in vertical, horizontal, diagonal (diagonal) columns It is designed so that you can do it.

[0013]   Specifically, as shown in FIG. 1, when the identification mark M is attached to the front surface side C, Both provide a frame B with a natural number N corresponding to the identification mark M on the back side D Then, the identification mark M attached to the front side C of the frame B is set according to a predetermined rule. By arranging in the grid A, the arrangement of the natural number N attached to the back side D of the frame B is It is configured to be a magic square.

[0014]   And in the case of the magic square created game board, the game board body in which the grid A is described, It is composed of tops B arranged on the game board body in which the above-mentioned grid A is described. There is.

[0015]   Next, a more detailed structure of the magic square making game board of the present invention is shown in FIG. A 4x4 grid created by arranging natural numbers (1, 2, 3, ..., 16) in a 4x4 grid Explain using the magic square.

[0016]   First, a natural number N (1, which is put into a 4 × 4 grid A that constitutes a 4 × 4 magic square 2, 3, ..., 16) is subtracted from each number to obtain an integer (0, 1, 2, ..., 15), Natural number 1 to integer 0, natural number 2 to integer 1, natural number 3 to integer 2, natural number 4 to integer 3, Natural number 5 to integer 4, natural number 6 to integer 5, natural number 7 to integer 6, natural number 8 to integer 7, Natural number 9 to integer 8, natural number 10 to integer 9, natural number 11 to integer 10, natural number 12 Integer 11, natural number 13 to integer 12, natural number 14 to integer 13, natural number 15 to integer 1 4, the integer 15 is associated with the natural number 16.

[0017]   Next, each of the above integers (0, 1, 2, ..., 15) is converted into a quaternary number, and an integer 0 for quaternion 00, integer 1 for quaternion 01, integer 2 for quaternion 02, integer 3 for quaternion 0 3, integer 4 to quaternary 10, integer 5 to quaternary 11, integer 6 to quaternary 12, integer 7 Quaternary 13, integer 8 to quaternary 20, integer 9 to quaternary 21, integer 10 to quaternary 22 , Integer 11 to quaternary number 23, integer 12 to quaternary number 30, integer 13 to quaternary number 31, integer 14 corresponds to a quaternary number 32, and integer 15 corresponds to a quaternary number 33.

[0018]   Next, the number of quartiles K in the above quaternary number is converted into the number of quartiles K (0, 1, 2, 3) The first classification for each (in the present embodiment, 0 is a symbol Δ, 1 is a symbol ◯, 2 is a symbol □, 3 Is classified according to the symbol ☆, and the number of ones digit in the quaternary number The second classification is performed for each L (0, 1, 2, 3) (in the present embodiment, 0 is the number of symbols 4, 1). Is classified by correlating the symbol number 1 and 2 with the symbol number 2 and 3 and the symbol number 3). And further, for each of the quaternary number K (0, 1, 2, 3), the first Combine the classification and the second classification for each ones digit L (0,1,2,3) in the quaternary number. The identification mark M corresponding to each of the quaternary numbers is formed by combining them. In the present embodiment, the symbols (△, ○, □, ☆) are added to each of the quaternary numbers. The identification mark M represented by the number of symbols (1, 2, 3, 4) corresponds (see Table 1). And

[0019]

[Table 1]

[0020]   Next, as shown in FIG. 2, the number K (0, 1, 2, Each 4 of 3) to each of the 4 x 4 grids, one each, vertical, horizontal, diagonal Arrange so that the sum of each column (diagonal line) is the same (so that the same numbers do not line up) Create a magic square, and then, as shown in Figure 3, the number of ones digit in the above quaternary number. Apply each of L (4 each of 0, 1, 2, 3) to each grid of 4 × 4 grid. Fit, vertical, horizontal, and diagonal (diagonal) columns so that their sums are equal (the same number should not line up). Create a magic square side by side.

[0021]   Further, the number of quartiles K (0,1) in the quaternary numbers shown in FIGS. , 4 each of 2, 3, and 3) and the number of ones in the quaternary number L (each of 0, 1, 2, 3 4 by synthesizing the two magic squares created by Create a quaternary magic square like this.

[0022]   And the quaternary numbers arranged in each square in the quaternary magic square shown in FIG. 4 above. Corresponding symbols (△, ○, □, ☆) and identification mark M represented by the number of symbols Is FIG. 5, and at this time, as is apparent from FIG. 5, in vertical, horizontal and diagonal (diagonal lines) , The symbols of the same kind are not lined up, and the number of each symbol is also different. The number of issues is 1, 2, 3, 4).

[0023]   Then, the identification mark M represented by the above-mentioned symbols (△, ○, □, ☆) and the number of symbols is Corresponds the integer (0, 1, 2, ..., 15) to the corresponding quaternary number, and then the above integer Corresponds natural numbers (1, 2, 3, ... 16) to (0, 1, 2, ..., 15) (see Table 1). )), And the identification mark represented by the above symbols (△, ○, □, ☆) and the number of symbols. By replacing M by a natural number N (1,2,3, ... 16) Such a 4 × 4 magic square is created.

[0024]   Moreover, as can be seen from the above procedure, is it a natural number N (1, 2, 3, ... 16)? The integer (0, 1, 2, ..., 15) obtained by subtracting 1 from the above is converted into a quaternary number, and the above quaternary number The first classification is performed for each quartile number K in, and for each quaternary digit L. The second classification is performed, and the first classification and the second classification are combined to form the second classification. When arranging the identified marks M one by one on each of the 4 × 4 grids A, the identification mark The same classification of the first classification in M must be lined up in vertical, horizontal, and diagonal (diagonal) columns. And the same classification of the second classification in the identification mark M is vertical, horizontal, After not aligning in diagonal (diagonal) columns, a natural number N is assigned to the identification mark M. By making it correspond, you can create a 4 × 4 magic square. There is no need to find the sum of the vertical, horizontal, and diagonal (diagonal) columns when creating the magic square You can easily create a 4x4 magic square.

[0025]   Further, as shown in FIG. 7, it is possible to combine the first classification and the second classification. Therefore, the identification mark M represented is referred to as a symbol (△, ○, □, ☆) in the present embodiment. For each of the identification marks M represented by the number of issues, a natural number N (1, 2, 3, ... 16) The identification number M to the natural number N It can be easily converted to (1, 2, 3, ..., 16), making it easier to convert 4x4 It is possible to create a magic square. By performing with the side D, it becomes easier to correspond the natural number N to the identification mark M. Of.

[0026]   And, FIG. 8 shows the 4 × 4 magic square created based on the above procedure. 2 is an example of the first classification in the identification mark M. Make sure that one classification does not line up in vertical, horizontal, and diagonal (diagonal) columns, If the same classification of the second classification in the block M is lined up in each row of vertical, horizontal and diagonal (diagonal line) Shows a 4 × 4 magic square with another arrangement obtained by arranging the identification marks M so that there is no ing.

[0027]   In addition, the knowledge formed by combining the first classification and the second classification described above. As the different mark M, not only the combination of the above-mentioned symbols and the number of symbols, but also a person, Characters and patterns such as marks that represent facial expressions such as animals, vehicles, emotions It's a good idea to use various classifications such as It is possible to promote the interest of children and students.

[0028]   9 and 10 show that the present invention is applied to each grid of the grid A of 5 × 5 with a natural number N. A 5 × 5 magic square created by arranging each number of (1, 2, 3, ..., 25) one by one In this case, the same procedure as in the case of the above 4 × 4 magic square is created. It is something.

[0029]   That is, first of all, the player who is placed in each of the 5 × 5 grids A that make up the 5 × 5 magic square The number N (1, 2, 3, ..., 25) is subtracted from each number to obtain an integer (0, 1, 2, ..., 25). 24), and the integers (0, 1, 2, ..., 25) are added to each of the natural numbers (1, 2, 3, ..., 25). 24) is made to correspond, and then the integers (0, 1, 2, ..., 24) are converted into a quinary number.

[0030]   Then, for each quintile (0, 1, 2, 3, 4) in the above-mentioned quinary number, the first minute Class (In the present embodiment, 0 is a symbol □, 1 is a symbol Δ, 2 is a symbol ○, 3 is a symbol ☆, 4 Is classified according to the symbol ◇, and the ones digit in the above-mentioned quinary number For each number (0, 1, 2, 3, 4) of the second classification (in this embodiment, 0 is the number of symbols). 5 and 1 correspond to the number of symbols 1 and 2 to the number of symbols 2 and 3 to the number of symbols 3 and 4 to the number of symbols 4 The quintile number (0, 1) , 2, 3, 4) and the number of ones digit (0, 1, 2, 3, 3) in the quinary number 4) Identification corresponding to each quinary number by combining each second classification The mark M is formed, and in the present embodiment, for each of the five-digit numbers, Identification represented by symbols (□, △, ○, ☆, ◇) and the number of symbols (1, 2, 3, 4, 5) The mark M corresponds (see Table 2).

[0031]

[Table 2]

[0032]   Also in this case, the identification mark M is on the front side C of the frame B and the natural number N is on the back side D. A natural number N (1, 2, 3, ..., 25) for each of the identification marks M. Correspond in advance to each other, and further, the identification mark M is the above-mentioned 4 × 4 magic A rule similar to the team, that is, the same classification of the first classification in the identification mark M is vertical, Do not line up in each row horizontally and diagonally (diagonally), and in the identification mark M Prevent the same classification of the second classification from lining up in vertical, horizontal, and diagonal (diagonal) columns By doing so, a 5 × 5 magic square can be easily created.

[0033]

[Effect of device]

  As described above in detail, the present invention has the following effects.   That is, according to the magic square making game board of the present invention, the identification mark is 4 × 4 or 5 × 5. When arranging the cells in the grid, the same classification of the first classification in the identification mark M is , The diagonal (diagonal) lines are not aligned, and the Arrange the same classifications of the two classifications so that they do not line up in vertical, horizontal, and diagonal (diagonal) columns. The magic square can be created by simply performing the calculation, and as a result, calculation is performed when creating the magic square. Since it is not necessary to do so, it will be easier for children and students to create magic squares. Yes, through the magic square, children and students can experience the mystery and fun of numbers, You can keep your interest in mathematics and mathematics at the same time, and at the same time, use the magic square It provides a means that can be done efficiently.

[Brief description of drawings]

FIG. 1 is a diagram showing a first example of a 4 × 4 magic square created by the present invention.

FIG. 2 is a diagram showing a magic square created by using the number of quartile in a quaternary number.

FIG. 3 is a diagram showing a magic square created by using the ones digit of a quaternary number.

FIG. 4 is a diagram showing a magic square created using a quaternary number.

FIG. 5 is a diagram showing a state in which an identification mark is associated with a quaternary number of a magic square created using a quaternary number.

FIG. 6 is a graph in which a natural number is associated with the identification mark
It is a figure which shows the magic square of * 4.

FIG. 7 is a diagram showing a correspondence between identification marks and natural numbers.

FIG. 8 is a diagram showing a second example of a 4 × 4 magic square created by the present invention.

FIG. 9 is a diagram showing a first example of a 5 × 5 magic square created by the present invention.

FIG. 10 is a diagram showing a second example of a 5 × 5 magic square created by the present invention.

[Explanation of symbols]

A n × n grid B frame Front side of C frame Back side of D frame K The number of fours in quaternion The number of ones in L quaternion M identification mark N natural number

Claims (2)

[Scope of utility model registration request] 1. A natural number N (natural number from 1 to 16) is arranged in each of the 4 × 4 grids A, and the natural number N is arranged in the 4 × 4 grid A. (1,
2, 3, ... 16) A magic square creation game board that creates magic squares arranged so that the sums of the vertical, horizontal, and diagonal columns are all equal. In the magic square creation game board, the magic square creation game board is 4 × Natural numbers N (1, 2, 3, ...
16) minus 1 from each number to obtain an integer (0, 1, 2, ... 1)
After obtaining 5), the integer (0,1,2, ... 15) is converted into a quaternary number, and further, for each quartile number (0,1,2,3). With the first classification,
Second for every ones digit (0, 1, 2, 3) in quaternary
After classifying, the first classification is performed for each fours digit (0, 1, 2, 3) in the above quaternary number, and the ones digit (0, 1, 2, 3) in quaternary number. The identification mark M corresponding to each of the quaternary numbers is formed by combining the second classification for each, and the natural number N (1, 2, 3, ... 16) is previously associated with the identification mark M. In addition, the same classification of the first classification in the identification mark M is not arranged in vertical, horizontal and diagonal (diagonal) columns, and the same classification of the second classification in the identification mark M is vertical. , The horizontal and diagonal (diagonal) columns are arranged so as not to be aligned, so that a 4 × 4 magic square is obtained, and the magic square making game board is 4 × 4.
The game board main body in which the grid A is described, and the frame B in which the identification mark M is attached to the front surface side C and the natural number N is attached to the back surface side D arranged on the 4 × 4 grid A described in the above game board main body A magic square creation game board characterized by consisting of. 2. A natural number N (natural number from 1 to 25) is arranged in each of the 5 × 5 grids A, and the natural number N is arranged in the 5 × 5 grid A. (1,
2, 3, ... 25) A magic square creation game board that creates magic squares arranged so that the sums of the vertical, horizontal, and diagonal columns are all equal. Natural numbers N (1, 2, 3, ...
25) minus 1 from each number to obtain an integer (0, 1, 2, ... 2)
After obtaining 4), the integer (0,1,2, ... 24) is converted into a quinary number, and the quintic number (0,1,2,3,4) in the quinary number is further converted. The first classification is performed for each and the ones digit in the quinary number (0, 1, 2, 3, 4)
After performing the second classification for each, the first classification for each quintic number (0, 1, 2, 3, 4) and the ones digit (0, The identification mark M corresponding to each of the quinary numbers is formed by combining the second classification for every 1, 2, 3, 4), and the natural number N (1, 2, 3) is previously added to the identification mark M. , 25) are made to correspond to each other, the same classification of the first classification in the identification mark M is not arranged in each of vertical, horizontal, and diagonal (diagonal) columns, and the second classification in the identification mark M is performed. By arranging the same categories of the above so that they do not line up in each of vertical, horizontal and diagonal (diagonal lines), it is possible to obtain a 5 × 5 magic square, and moreover, the above magic square making game board. Is written on the game board body in which the 5 × 5 grid A is described and on the above game board body. A magic square making game board characterized by comprising a top side C arranged on a 5 × 5 grid A and a piece B having an identification mark M on the front side C and a natural number N on the back side D.