Conference rusure::math

537.0. "More on Magic Squares" by VOGON::CATTERMOUL (Richard REO F/M8 830-4564) Mon Jul 14 1986 12:36

		Producing the Real 4-Cube

Remember the Rubik's cube, in particular his 4-cube. Using the positions
of numbers in the basic 4x4 magic square, six 4x4 magic squares can easily 
be generated from the numbers 1 to 96.

The basic 4x4 is:
			 9 12  6  7
                         8  5 11 10
                        15 14  4  1
                         2  3 13 16

Simply take the numbers 1 to 96 and arrange them thus:
        
	1 12 13 24 25 36 37 48 49 60 61 72 73 84 85 96
        2 11 14 23 26 35 38 47 50 59 62 71 74 83 86 95
        3 10 15 22 27 34 39 46 51 58 63 70 75 82 87 94
        4  9 16 21 28 34 40 45 52 57 64 69 76 81 88 93
        5  8 17 20 29 32 41 44 53 56 65 68 77 80 89 92
        6  7 18 19 30 31 42 43 54 55 66 67 78 79 90 91

Thus, we have 6 groups of 16 numbers. The magic sum is (1+96)*2 = 194.
For each group, position each number according to the 4x4 given above.
The result is:

49 72 36 37  50 71 35 38  51 70 34 39  52 69 34 40  53 68 32 41  54 67 31 42
48 25 61 60  47 26 62 59  46 27 63 58  45 28 64 57  44 29 65 53  43 30 66 55
85 84 24  1  86 83 23  2  87 82 22  3  88 81 21  4  89 80 20  5  90 79 19  6
12 13 73 96  11 14 74 95  10 15 75 94   9 16 76 93   8 17 77 92   7 18 78 91

Richard Cattermoul