CUADRADOS SUPERMÁGICOS DE TAMAÑO CUATRO
The aim of this paper is to obtain all magic squares of size four, by using an Optimization Model where, in addition to the traditional restrictions (sums for rows, columns and diagonals), other restrictions related to four 2 x 2 submatrices, into which the square can be divided, are taken into acco...
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| Format: | Article |
| Language: | Spanish |
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Executive Business School
2020-08-01
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| Series: | Avances en Ciencias e Ingeniería |
| Subjects: | |
| Online Access: | https://www.executivebs.org/publishing.cl/avances-en-ciencias-e-ingenieria-vol-11-nro-3-ano-2020-articulo-8/ |
| _version_ | 1818998843172192256 |
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| author | Vicente F. Molina-Padrón |
| author_facet | Vicente F. Molina-Padrón |
| author_sort | Vicente F. Molina-Padrón |
| collection | DOAJ |
| description | The aim of this paper is to obtain all magic squares of size four, by using an Optimization Model where, in addition to the traditional restrictions (sums for rows, columns and diagonals), other restrictions related to four 2 x 2 submatrices, into which the square can be divided, are taken into account. It is shown that these additional restrictions are included in the traditional ones; therefore, all squares of size four could be classified as supermagic. The problem is represented by means of a Linear Programming Model in Integers with multiple solutions; which, when solved with the help of LINGO software, allowed to find the 880 squares that meet such restrictions. The way squares are presented makes it easy to locate them from characteristics referred to the position of number one. The different combinations for number one in any row for which these squares do not exist, are ordered. |
| first_indexed | 2024-12-20T22:07:58Z |
| format | Article |
| id | doaj.art-d5db57de4d464b81bff249acc9169ee7 |
| institution | Directory Open Access Journal |
| issn | 0718-8706 |
| language | Spanish |
| last_indexed | 2024-12-20T22:07:58Z |
| publishDate | 2020-08-01 |
| publisher | Executive Business School |
| record_format | Article |
| series | Avances en Ciencias e Ingeniería |
| spelling | doaj.art-d5db57de4d464b81bff249acc9169ee72022-12-21T19:25:14ZspaExecutive Business SchoolAvances en Ciencias e Ingeniería0718-87062020-08-0111381107CUADRADOS SUPERMÁGICOS DE TAMAÑO CUATROVicente F. Molina-Padrón0Universidad Central “Marta Abreu” de Las Villas, Facultad de Matemática, Física y ComputaciónThe aim of this paper is to obtain all magic squares of size four, by using an Optimization Model where, in addition to the traditional restrictions (sums for rows, columns and diagonals), other restrictions related to four 2 x 2 submatrices, into which the square can be divided, are taken into account. It is shown that these additional restrictions are included in the traditional ones; therefore, all squares of size four could be classified as supermagic. The problem is represented by means of a Linear Programming Model in Integers with multiple solutions; which, when solved with the help of LINGO software, allowed to find the 880 squares that meet such restrictions. The way squares are presented makes it easy to locate them from characteristics referred to the position of number one. The different combinations for number one in any row for which these squares do not exist, are ordered.https://www.executivebs.org/publishing.cl/avances-en-ciencias-e-ingenieria-vol-11-nro-3-ano-2020-articulo-8/lingomagic square 4 x 4optimization modelsymmetry properties |
| spellingShingle | Vicente F. Molina-Padrón CUADRADOS SUPERMÁGICOS DE TAMAÑO CUATRO Avances en Ciencias e Ingeniería lingo magic square 4 x 4 optimization model symmetry properties |
| title | CUADRADOS SUPERMÁGICOS DE TAMAÑO CUATRO |
| title_full | CUADRADOS SUPERMÁGICOS DE TAMAÑO CUATRO |
| title_fullStr | CUADRADOS SUPERMÁGICOS DE TAMAÑO CUATRO |
| title_full_unstemmed | CUADRADOS SUPERMÁGICOS DE TAMAÑO CUATRO |
| title_short | CUADRADOS SUPERMÁGICOS DE TAMAÑO CUATRO |
| title_sort | cuadrados supermagicos de tamano cuatro |
| topic | lingo magic square 4 x 4 optimization model symmetry properties |
| url | https://www.executivebs.org/publishing.cl/avances-en-ciencias-e-ingenieria-vol-11-nro-3-ano-2020-articulo-8/ |
| work_keys_str_mv | AT vicentefmolinapadron cuadradossupermagicosdetamanocuatro |