How to create Magic Squares Let’s make some magic! Diana Gonzalez Lauren Nation Kristy Ochoa Cindy Santiago By PresenterMedia.com

DOUBLe-Even Magic Squares

Steps to solving double-even magic squares Fill in numbers 1 through n2, right to left, beginning at the bottom corner. When you reach the end of the first row, continue numbering beginning on the right side of the next row 17 16 15 14 13 12 11 10 9

Steps to solving double-even magic squares Divide your grid into 16 mxm grids. To find m: n2/16 The 4 mxm corner squares the 4 mxm inner squares will not change. We will work on the left over rectangles.

Steps to solving double-even magic squares Now we’re going to reflect the the rectangles to the opposite side. We have now completed the square. We can check it by computing the sum of the rows, columns, and diagonals.

Example of a 12 X 12 Magic Square

Using de la Loubere method Odd Magic Squares Using de la Loubere method

Steps to solving odd magic squares 31 40 49 2 11 20 If there is a number blocking the next corresponding square, place the number directly below the last placed number and continue numbering. Begin by placing 1 in the middle square of the first row. 39 1 30 48 10 19 28 We will place the following numbers in the squares diagonally above and to the right. 47 7 9 18 27 29 38 Special Rule!! When you reach the top, right corner square, place the next number in the square directly below it. 6 8 17 26 35 37 46 If there isn’t a column available for a number to be placed, move it to the last square of the corresponding column. 34 36 45 14 16 25 5 15 24 33 42 44 4 13 Continue numbering through the diagonal. 23 32 41 43 3 12 21 If there isn’t a row available for a number to be placed, move it to the first square of the corresponding row. 22