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).

They are

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.



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