By Trent Lynch

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**Extra resources for Recreational Mathematics**

**Example text**

Step 2 1 . step 3 1 step 4 1 3 2 2 3 4 2 step 5 1 3 5 4 2 step 6 1 6 3 5 4 2 step 7 1 6 3 5 7 4 2 step 8 8 1 6 3 5 7 4 2 step 9 8 1 6 3 5 7 4 9 2 Starting from other squares rather than the central column of the first row is possible, but then only the row and column sums will be identical and result in a magic sum, whereas the diagonal sums will differ. The result will thus be a semimagic square and not a true magic square. Moving in directions other than north east can also result in magic squares.

E. x+9y where x is the original number and y is a number from 0 to 3, following the pattern of the medjig-square. Example: Order 3 8 1 6 3 5 7 4 9 2 2 1 3 0 3 0 Medjig 3 x 3 3 0 2 0 0 3 1 3 1 1 2 2 2 0 3 3 2 2 0 0 1 3 1 1 2 1 0 1 2 3 26 17 30 3 31 4 35 8 12 21 22 13 Order 6 1 19 28 10 14 23 5 32 27 9 36 18 6 33 25 34 2 11 24 15 7 16 20 29 Similarly, for any larger integer N, a magic square of order 2N can be constructed from any N x N medjig-square with each row, column, and long diagonal summing to (N1)*N/2, and any N x N magic square (using the four numbers from 1 to 4N^2 that equal the original number modulo N^2).

There are 18 squares, with each sequence occurring 3 times. The aim of the puzzle is to take 9 squares out of the collection and arrange them in a 3 x 3 "medjig-square" in such a way that each row and column formed by the quadrants sums to 9, along with the two long diagonals. The medjig method of constructing a magic square of order 6 is as follows: Construct any 3 x 3 medjig-square (ignoring the original game's limit on the number of times that a given sequence is used). Take the 3 x 3 magic square and divide each of its squares into four quadrants.