Some theorems on construction of magic squares

✍ Scribed by Y.H. Ku; Nan-Xian Chen

• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 661 KB
• Volume: 322
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(86)90031-1

✦ Synopsis

Four theorems are given on the construction of magic squares. Theorem Iproves that substituting the number k in a N x N magic square by the kth incremental square of a m x m magic square, the resultant mN x mN square is a magic square. Theorem il shows that dividing an even rank N x N magic square into four quadrants, substituting the number k in the odd-number quadrants by the kth incremental square of a type-l simple square and substituting the number k in the even-number quadrants by the kth incremental square of a type-2 simple square, the resultant mN x mN square is a magic square. In an even rank N x N magic square, Theorem III proves that substituting the number k = A, by the kth incremental simple square of type-l or type-2, depending on the sum of it-j even or odd, the resultant square is a magic square. Theorem IV shows that in an even rank N x N magic square with each row and eack column having an equal number of odd and even numbers, substituting for odd numbers by the ktk incremental simple square of type-l and for even numbers by the kth incremental simple square of type-2, the resultant square is a magic square. Sixteen examples are given.