### Half pandiagonal 5x5x5 magic cube (Shift method)

See on www.trump.de/magic-squares/magic-cubes/cubes-1.html the following diagonal magic 5x5x5 cube.

 The first known perfect magic cube of order 5 Walter Trump and Christian Boyer, 2003-11-13

This 5x5x5 magic cube has as magic features:

• the 5 rows, the 5 columns and the 2 diagonals in each level give the magic sum of 315;
• the 25 pilars give the magic sum of 315;
• the 20 diagonals through the 5 levels give the magic sum of 315 (e.g. 115+64+38+87+11=315 or 106+44+58+87+20=315);
• the 4 tridiagonals give the magic sum of 315 (e.g. 67+39+63+87+59=315).

Use the same method to construct the panmagic 5x5 square (shift) to construct a symmetric & semi panmagic 5x5x5 cube.

Choose as first row of the first grid in the first level: 2-3-4-0-1. Construct row 2 up to 5 of the first grid of the first level by shifting the first row each time 2 places to the left. Construct the first grid of level 2 up to 5 by shifting the columns of the first grid of the first level each time 2 places to the left.

Choose as first row of the second grid in the first level: 0-1-2-3-4. Construct row 2 up to 5 of the second grid of the first level by shifting the first row each time 2 places to the right. Construct the second grid of level 2 up to 5 by shifting the columns of the second grid of the first level each time 2 places to the left.

The third grid is the same as the second grid, but the levels must be put in reversed order (5 up to 1 instead of 1 up to 5).

Take 1x number from first grid + 5x number from second grid + 25x number from third grid to get a symmetric & semi (pan)magic 5x5x5 cube.

 1x number +1          +    5x number               +    25x number              =    5x5x5 cube, first level 2 3 4 0 1 0 1 2 3 4 3 4 0 1 2 78 109 15 41 72 4 0 1 2 3 3 4 0 1 2 1 2 3 4 0 45 71 77 108 14 1 2 3 4 0 1 2 3 4 0 4 0 1 2 3 107 13 44 75 76 3 4 0 1 2 4 0 1 2 3 2 3 4 0 1 74 80 106 12 43 0 1 2 3 4 2 3 4 0 1 0 1 2 3 4 11 42 73 79 110 1x number +1         +    5x number                +    25x number             =    5x5x5 cube, second level 4 0 1 2 3 2 3 4 0 1 1 2 3 4 0 40 66 97 103 9 1 2 3 4 0 0 1 2 3 4 4 0 1 2 3 102 8 39 70 96 3 4 0 1 2 3 4 0 1 2 2 3 4 0 1 69 100 101 7 38 0 1 2 3 4 1 2 3 4 0 0 1 2 3 4 6 37 68 99 105 2 3 4 0 1 4 0 1 2 3 3 4 0 1 2 98 104 10 36 67 1x number +1         +    5x number                +    25x number             =    5x5x5 cube, third level 1 2 3 4 0 4 0 1 2 3 4 0 1 2 3 122 3 34 65 91 3 4 0 1 2 2 3 4 0 1 2 3 4 0 1 64 95 121 2 33 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 1 32 63 94 125 2 3 4 0 1 3 4 0 1 2 3 4 0 1 2 93 124 5 31 62 4 0 1 2 3 1 2 3 4 0 1 2 3 4 0 35 61 92 123 4 1x nmber +1           +    5x number                +    25x number              =    5x5x5 cube, fourth level 3 4 0 1 2 1 2 3 4 0 2 3 4 0 1 59 90 116 22 28 0 1 2 3 4 4 0 1 2 3 0 1 2 3 4 21 27 58 89 120 2 3 4 0 1 2 3 4 0 1 3 4 0 1 2 88 119 25 26 57 4 0 1 2 3 0 1 2 3 4 1 2 3 4 0 30 56 87 118 24 1 2 3 4 0 3 4 0 1 2 4 0 1 2 3 117 23 29 60 86 1x number +1         +    5x number                +    25x number             =    5x5x5 cube, fifth level 0 1 2 3 4 3 4 0 1 2 0 1 2 3 4 16 47 53 84 115 2 3 4 0 1 1 2 3 4 0 3 4 0 1 2 83 114 20 46 52 4 0 1 2 3 4 0 1 2 3 1 2 3 4 0 50 51 82 113 19 1 2 3 4 0 2 3 4 0 1 4 0 1 2 3 112 18 49 55 81 3 4 0 1 2 0 1 2 3 4 2 3 4 0 1 54 85 111 17 48

Less & extra magic features:

• The vertical diagonals through the levels give not the magic sum;
• The pandiagonals in each level give the magic sum of 315;
• The horizontal pandiagonals through the levels give the magic sum of 315

Use the shift method to construct magic cubes of odd order and from 9x9x9 and up the result is Nasik. See on this website the shift method for:

5x5x5, semi [pan]magic 5x5x5 cube.xls