I'm trying to work out the most even distribution of a set of numbers across the faces of a cube.
The numbers are 1-24 and I wish to place 1 number in reach corner of each face.
On a standard die, all opposing faces sum to 7, so I figured that I would want the numbers on opposite corners to sum to 25.
The total sum of the numbers 1-24 is 300, which divides evenly to a total of 50 a face.
Based on that, I've managed to create the following 6 sets that obey the above "rules" (However there may be at least one set of alternative set of faces).
1 12 16 21 opp 24 13 9 4
2 11 17 20 opp 23 14 8 5
3 10 18 19 opp 22 15 7 6
Additionally I was hoping to get all the corners to be equal too (where the 3 faces join)
300 doesn't divide equally by 8, but it does by 4.
With that in mind, I feel it should be possible for adjacent corners, and the corners diagonally opposite through the cube to total 75. And opposite corners on a face to total 74 or 76 (with individual corner totals of 37 and 38).
But this is where I'm getting tied up. I can get a couple of corners to sum to 37/38 and have some of their relevant opposites also match up, but then I get lost.