CUADRADOS SUPERMÁGICOS DE TAMAÑO CUATRO

Avances en Ciencias e Ingeniería

Vicente F. Molina-Padrón¹ 

[1] Universidad Central “Marta Abreu” de Las Villas, Facultad de Matemática, Física y Computación;

关键词: lingo;    magic square 4 x 4;    optimization model;    symmetry properties;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown