{"id":2318,"date":"2022-05-28T21:25:10","date_gmt":"2022-05-29T00:25:10","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=2318"},"modified":"2023-11-15T21:03:07","modified_gmt":"2023-11-16T00:03:07","slug":"magic-and-semi-magic-squares-with-blocks-of-magic-rectangles","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=2318","title":{"rendered":"Magic Rectangles in Construction of Magic and Block-Bordered Magic Squares: Part 1 – Even and Odd Orders Magic Squares"},"content":{"rendered":"\n

In this work, blocks of magic rectangles<\/strong> with equal and unequal sums<\/strong> are used to construct magic squares. The equal sum blocks magic rectangles<\/strong> lead us to even order<\/strong> magic squares, such as, of orders 8, 12, 16, 20, 24, 28, 32, 36, 40, 42, 44 and 48. These magic squares are constructed using magic rectangles<\/strong> of orders 2×4, 2×14, 4×6, 6×10, 6×14<\/strong>, etc. There is only one example of an even order magic square with different sums blocks of magic rectangles<\/strong>, i.e., of order eighteen. The odd order<\/strong> magic squares are with unequal sum blocks magic rectangles<\/strong>. These are of orders 15, 21, 27, 33, 39 and 45. These are constructed using magic rectangles of orders 3×5, 3×7, 3×9, 3×11, 3×13, 3×15, 5×7<\/strong>, etc. The magic squares of orders 12, 20, 24, 28, 42, 45 and 48 are written in two ways. These magic squares are used to bring block bordered<\/strong> magic squares<\/strong>. These block-bordered<\/strong> are of orders 10, 14, 17, 19, 22, 23, 26, 29, 31, 34, 37, 38, 41, 43, 46 and 47.  Most of the magic squares from order 8 to 48 are studied in this work, except the orders 9, 11, 13 and 25. These are already studied by the author in another work<\/a><\/p>\n\n\n\n

Link for downloading the work:<\/p>\n\n\n\n