Franklin panmagic 16x16x16 cube (2)

 

Use a 4x4 panmagic square to construct a Franklin panmagic 16x16x16 cube.

 

 

Take 1x digit from first grid [level 1]

1 8 13 12 1 8 13 12 1 8 13 12 1 8 13 12
15 10 3 6 15 10 3 6 15 10 3 6 15 10 3 6
4 5 16 9 4 5 16 9 4 5 16 9 4 5 16 9
14 11 2 7 14 11 2 7 14 11 2 7 14 11 2 7
1 8 13 12 1 8 13 12 1 8 13 12 1 8 13 12
15 10 3 6 15 10 3 6 15 10 3 6 15 10 3 6
4 5 16 9 4 5 16 9 4 5 16 9 4 5 16 9
14 11 2 7 14 11 2 7 14 11 2 7 14 11 2 7
1 8 13 12 1 8 13 12 1 8 13 12 1 8 13 12
15 10 3 6 15 10 3 6 15 10 3 6 15 10 3 6
4 5 16 9 4 5 16 9 4 5 16 9 4 5 16 9
14 11 2 7 14 11 2 7 14 11 2 7 14 11 2 7
1 8 13 12 1 8 13 12 1 8 13 12 1 8 13 12
15 10 3 6 15 10 3 6 15 10 3 6 15 10 3 6
4 5 16 9 4 5 16 9 4 5 16 9 4 5 16 9
14 11 2 7 14 11 2 7 14 11 2 7 14 11 2 7

 

 

+ 16x digit from second grid [level 1]

0 3 3 0 3 0 0 3 1 2 2 1 2 1 1 2
3 0 0 3 0 3 3 0 2 1 1 2 1 2 2 1
0 3 3 0 3 0 0 3 1 2 2 1 2 1 1 2
3 0 0 3 0 3 3 0 2 1 1 2 1 2 2 1
0 3 3 0 3 0 0 3 1 2 2 1 2 1 1 2
3 0 0 3 0 3 3 0 2 1 1 2 1 2 2 1
0 3 3 0 3 0 0 3 1 2 2 1 2 1 1 2
3 0 0 3 0 3 3 0 2 1 1 2 1 2 2 1
0 3 3 0 3 0 0 3 1 2 2 1 2 1 1 2
3 0 0 3 0 3 3 0 2 1 1 2 1 2 2 1
0 3 3 0 3 0 0 3 1 2 2 1 2 1 1 2
3 0 0 3 0 3 3 0 2 1 1 2 1 2 2 1
0 3 3 0 3 0 0 3 1 2 2 1 2 1 1 2
3 0 0 3 0 3 3 0 2 1 1 2 1 2 2 1
0 3 3 0 3 0 0 3 1 2 2 1 2 1 1 2
3 0 0 3 0 3 3 0 2 1 1 2 1 2 2 1

 

 

+ 64x digit from third grid [level 1]

0 3 0 3 0 3 0 3 0 3 0 3 0 3 0 3
3 0 3 0 3 0 3 0 3 0 3 0 3 0 3 0
3 0 3 0 3 0 3 0 3 0 3 0 3 0 3 0
0 3 0 3 0 3 0 3 0 3 0 3 0 3 0 3
3 0 3 0 3 0 3 0 3 0 3 0 3 0 3 0
0 3 0 3 0 3 0 3 0 3 0 3 0 3 0 3
0 3 0 3 0 3 0 3 0 3 0 3 0 3 0 3
3 0 3 0 3 0 3 0 3 0 3 0 3 0 3 0
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1

 

 

+ 256x digit from fourth grid [level 1]

1 1 16 16 1 1 16 16 1 1 16 16 1 1 16 16
16 16 1 1 16 16 1 1 16 16 1 1 16 16 1 1
1 1 16 16 1 1 16 16 1 1 16 16 1 1 16 16
16 16 1 1 16 16 1 1 16 16 1 1 16 16 1 1
1 1 16 16 1 1 16 16 1 1 16 16 1 1 16 16
16 16 1 1 16 16 1 1 16 16 1 1 16 16 1 1
1 1 16 16 1 1 16 16 1 1 16 16 1 1 16 16
16 16 1 1 16 16 1 1 16 16 1 1 16 16 1 1
1 1 16 16 1 1 16 16 1 1 16 16 1 1 16 16
16 16 1 1 16 16 1 1 16 16 1 1 16 16 1 1
1 1 16 16 1 1 16 16 1 1 16 16 1 1 16 16
16 16 1 1 16 16 1 1 16 16 1 1 16 16 1 1
1 1 16 16 1 1 16 16 1 1 16 16 1 1 16 16
16 16 1 1 16 16 1 1 16 16 1 1 16 16 1 1
1 1 16 16 1 1 16 16 1 1 16 16 1 1 16 16
16 16 1 1 16 16 1 1 16 16 1 1 16 16 1 1

 

 

= Franklin panmagic 16x16x16 cube [level 1]

1 248 3901 4044 49 200 3853 4092 17 232 3885 4060 33 216 3869 4076
4095 3850 195 54 4047 3898 243 6 4079 3866 211 38 4063 3882 227 22
196 53 4096 3849 244 5 4048 3897 212 37 4080 3865 228 21 4064 3881
3902 4043 2 247 3854 4091 50 199 3886 4059 18 231 3870 4075 34 215
193 56 4093 3852 241 8 4045 3900 209 40 4077 3868 225 24 4061 3884
3903 4042 3 246 3855 4090 51 198 3887 4058 19 230 3871 4074 35 214
4 245 3904 4041 52 197 3856 4089 20 229 3888 4057 36 213 3872 4073
4094 3851 194 55 4046 3899 242 7 4078 3867 210 39 4062 3883 226 23
65 184 3965 3980 113 136 3917 4028 81 168 3949 3996 97 152 3933 4012
4031 3914 131 118 3983 3962 179 70 4015 3930 147 102 3999 3946 163 86
132 117 4032 3913 180 69 3984 3961 148 101 4016 3929 164 85 4000 3945
3966 3979 66 183 3918 4027 114 135 3950 3995 82 167 3934 4011 98 151
129 120 4029 3916 177 72 3981 3964 145 104 4013 3932 161 88 3997 3948
3967 3978 67 182 3919 4026 115 134 3951 3994 83 166 3935 4010 99 150
68 181 3968 3977 116 133 3920 4025 84 165 3952 3993 100 149 3936 4009
4030 3915 130 119 3982 3963 178 71 4014 3931 146 103 3998 3947 162 87

 

 

Each level consists of 16 proportional panmagic 4x4 squares. The cube is in each level panmagic and 2x2 compact and each 1/4 row/column/diagonal gives 1/4 of the magic sum. The cube is pandiagonal and pantriagonal magic through the levels and each 1/4 pillar gives 1/4 of the magic sum and each 1/2 tridiagonal gives 1/2 of the magic sum.

 

See all grids and all levels of the 16x16x16 magic cube in the downloads below.

 

 

Download
16x16x16, Franklin panmagic 16x16x16 cub
Microsoft Excel werkblad 696.0 KB
Download
16x16x16, Franklin panmagic 16x16x16 cub
Microsoft Excel werkblad 809.5 KB