Magic: now your problem is to decide how to choose amongst the thousands of possibilities
The solution I posted above is a bit unsatisfactory in a way: there is a band of pairs of numbers going around the cube:
(1,24),(8,17),(12,13),(14,11),(21,4),(20,5),(15,10),(9,16)
Each pair adds up to 25. Then the remaining two faces of the cube have "orthogonally opposite" numbers adding to 25. This is a nice pattern in a way, but not that symmetric.
Does every solution look like this?
Here are the first 100 solutions, listed in the order given in the previous post. There are obvious patterns of solutions that differ only very slightly.
[1, 8, 17, 24, 9, 16, 10, 15, 19, 7, 2, 22, 4, 5, 20, 21, 11, 14, 12, 13, 23, 3, 6, 18]
[1, 8, 17, 24, 9, 16, 10, 15, 19, 7, 2, 22, 4, 5, 20, 21, 13, 12, 14, 11, 23, 3, 6, 18]
[1, 8, 17, 24, 9, 16, 10, 15, 19, 7, 2, 22, 5, 4, 21, 20, 11, 14, 12, 13, 23, 3, 6, 18]
[1, 8, 17, 24, 9, 16, 10, 15, 19, 7, 2, 22, 5, 4, 21, 20, 13, 12, 14, 11, 23, 3, 6, 18]
[1, 8, 17, 24, 9, 16, 10, 15, 20, 6, 3, 21, 2, 7, 18, 23, 11, 14, 12, 13, 22, 4, 5, 19]
[1, 8, 17, 24, 9, 16, 10, 15, 20, 6, 3, 21, 2, 7, 18, 23, 13, 12, 14, 11, 22, 4, 5, 19]
[1, 8, 17, 24, 9, 16, 10, 15, 20, 6, 3, 21, 7, 2, 23, 18, 11, 14, 12, 13, 22, 4, 5, 19]
[1, 8, 17, 24, 9, 16, 10, 15, 20, 6, 3, 21, 7, 2, 23, 18, 13, 12, 14, 11, 22, 4, 5, 19]
[1, 8, 17, 24, 9, 16, 10, 15, 22, 4, 5, 19, 2, 7, 18, 23, 11, 14, 12, 13, 20, 6, 3, 21]
[1, 8, 17, 24, 9, 16, 10, 15, 22, 4, 5, 19, 2, 7, 18, 23, 13, 12, 14, 11, 20, 6, 3, 21]
[1, 8, 17, 24, 9, 16, 10, 15, 22, 4, 5, 19, 7, 2, 23, 18, 11, 14, 12, 13, 20, 6, 3, 21]
[1, 8, 17, 24, 9, 16, 10, 15, 22, 4, 5, 19, 7, 2, 23, 18, 13, 12, 14, 11, 20, 6, 3, 21]
[1, 8, 17, 24, 9, 16, 10, 15, 23, 3, 6, 18, 4, 5, 20, 21, 11, 14, 12, 13, 19, 7, 2, 22]
[1, 8, 17, 24, 9, 16, 10, 15, 23, 3, 6, 18, 4, 5, 20, 21, 13, 12, 14, 11, 19, 7, 2, 22]
[1, 8, 17, 24, 9, 16, 10, 15, 23, 3, 6, 18, 5, 4, 21, 20, 11, 14, 12, 13, 19, 7, 2, 22]
[1, 8, 17, 24, 9, 16, 10, 15, 23, 3, 6, 18, 5, 4, 21, 20, 13, 12, 14, 11, 19, 7, 2, 22]
[1, 8, 17, 24, 9, 16, 11, 14, 20, 7, 2, 21, 3, 6, 19, 22, 10, 15, 12, 13, 23, 4, 5, 18]
[1, 8, 17, 24, 9, 16, 11, 14, 20, 7, 2, 21, 3, 6, 19, 22, 13, 12, 15, 10, 23, 4, 5, 18]
[1, 8, 17, 24, 9, 16, 11, 14, 20, 7, 2, 21, 6, 3, 22, 19, 10, 15, 12, 13, 23, 4, 5, 18]
[1, 8, 17, 24, 9, 16, 11, 14, 20, 7, 2, 21, 6, 3, 22, 19, 13, 12, 15, 10, 23, 4, 5, 18]
[1, 8, 17, 24, 9, 16, 11, 14, 21, 6, 3, 20, 2, 7, 18, 23, 10, 15, 12, 13, 22, 5, 4, 19]
[1, 8, 17, 24, 9, 16, 11, 14, 21, 6, 3, 20, 2, 7, 18, 23, 13, 12, 15, 10, 22, 5, 4, 19]
[1, 8, 17, 24, 9, 16, 11, 14, 21, 6, 3, 20, 7, 2, 23, 18, 10, 15, 12, 13, 22, 5, 4, 19]
[1, 8, 17, 24, 9, 16, 11, 14, 21, 6, 3, 20, 7, 2, 23, 18, 13, 12, 15, 10, 22, 5, 4, 19]
[1, 8, 17, 24, 9, 16, 11, 14, 22, 5, 4, 19, 2, 7, 18, 23, 10, 15, 12, 13, 21, 6, 3, 20]
[1, 8, 17, 24, 9, 16, 11, 14, 22, 5, 4, 19, 2, 7, 18, 23, 13, 12, 15, 10, 21, 6, 3, 20]
[1, 8, 17, 24, 9, 16, 11, 14, 22, 5, 4, 19, 7, 2, 23, 18, 10, 15, 12, 13, 21, 6, 3, 20]
[1, 8, 17, 24, 9, 16, 11, 14, 22, 5, 4, 19, 7, 2, 23, 18, 13, 12, 15, 10, 21, 6, 3, 20]
[1, 8, 17, 24, 9, 16, 11, 14, 23, 4, 5, 18, 3, 6, 19, 22, 10, 15, 12, 13, 20, 7, 2, 21]
[1, 8, 17, 24, 9, 16, 11, 14, 23, 4, 5, 18, 3, 6, 19, 22, 13, 12, 15, 10, 20, 7, 2, 21]
[1, 8, 17, 24, 9, 16, 11, 14, 23, 4, 5, 18, 6, 3, 22, 19, 10, 15, 12, 13, 20, 7, 2, 21]
[1, 8, 17, 24, 9, 16, 11, 14, 23, 4, 5, 18, 6, 3, 22, 19, 13, 12, 15, 10, 20, 7, 2, 21]
[1, 8, 17, 24, 9, 16, 13, 12, 22, 7, 2, 19, 4, 5, 20, 21, 10, 15, 14, 11, 23, 6, 3, 18]
[1, 8, 17, 24, 9, 16, 13, 12, 22, 7, 2, 19, 4, 5, 20, 21, 11, 14, 15, 10, 23, 6, 3, 18]
[1, 8, 17, 24, 9, 16, 13, 12, 22, 7, 2, 19, 5, 4, 21, 20, 10, 15, 14, 11, 23, 6, 3, 18]
[1, 8, 17, 24, 9, 16, 13, 12, 22, 7, 2, 19, 5, 4, 21, 20, 11, 14, 15, 10, 23, 6, 3, 18]
[1, 8, 17, 24, 9, 16, 13, 12, 23, 6, 3, 18, 4, 5, 20, 21, 10, 15, 14, 11, 22, 7, 2, 19]
[1, 8, 17, 24, 9, 16, 13, 12, 23, 6, 3, 18, 4, 5, 20, 21, 11, 14, 15, 10, 22, 7, 2, 19]
[1, 8, 17, 24, 9, 16, 13, 12, 23, 6, 3, 18, 5, 4, 21, 20, 10, 15, 14, 11, 22, 7, 2, 19]
[1, 8, 17, 24, 9, 16, 13, 12, 23, 6, 3, 18, 5, 4, 21, 20, 11, 14, 15, 10, 22, 7, 2, 19]
[1, 8, 17, 24, 10, 15, 9, 16, 18, 6, 3, 23, 4, 5, 20, 21, 12, 13, 11, 14, 22, 2, 7, 19]
[1, 8, 17, 24, 10, 15, 9, 16, 18, 6, 3, 23, 4, 5, 20, 21, 14, 11, 13, 12, 22, 2, 7, 19]
[1, 8, 17, 24, 10, 15, 9, 16, 18, 6, 3, 23, 5, 4, 21, 20, 12, 13, 11, 14, 22, 2, 7, 19]
[1, 8, 17, 24, 10, 15, 9, 16, 18, 6, 3, 23, 5, 4, 21, 20, 14, 11, 13, 12, 22, 2, 7, 19]
[1, 8, 17, 24, 10, 15, 9, 16, 19, 5, 4, 22, 2, 7, 18, 23, 12, 13, 11, 14, 21, 3, 6, 20]
[1, 8, 17, 24, 10, 15, 9, 16, 19, 5, 4, 22, 2, 7, 18, 23, 14, 11, 13, 12, 21, 3, 6, 20]
[1, 8, 17, 24, 10, 15, 9, 16, 19, 5, 4, 22, 7, 2, 23, 18, 12, 13, 11, 14, 21, 3, 6, 20]
[1, 8, 17, 24, 10, 15, 9, 16, 19, 5, 4, 22, 7, 2, 23, 18, 14, 11, 13, 12, 21, 3, 6, 20]
[1, 8, 17, 24, 10, 15, 9, 16, 21, 3, 6, 20, 2, 7, 18, 23, 12, 13, 11, 14, 19, 5, 4, 22]
[1, 8, 17, 24, 10, 15, 9, 16, 21, 3, 6, 20, 2, 7, 18, 23, 14, 11, 13, 12, 19, 5, 4, 22]
[1, 8, 17, 24, 10, 15, 9, 16, 21, 3, 6, 20, 7, 2, 23, 18, 12, 13, 11, 14, 19, 5, 4, 22]
[1, 8, 17, 24, 10, 15, 9, 16, 21, 3, 6, 20, 7, 2, 23, 18, 14, 11, 13, 12, 19, 5, 4, 22]
[1, 8, 17, 24, 10, 15, 9, 16, 22, 2, 7, 19, 4, 5, 20, 21, 12, 13, 11, 14, 18, 6, 3, 23]
[1, 8, 17, 24, 10, 15, 9, 16, 22, 2, 7, 19, 4, 5, 20, 21, 14, 11, 13, 12, 18, 6, 3, 23]
[1, 8, 17, 24, 10, 15, 9, 16, 22, 2, 7, 19, 5, 4, 21, 20, 12, 13, 11, 14, 18, 6, 3, 23]
[1, 8, 17, 24, 10, 15, 9, 16, 22, 2, 7, 19, 5, 4, 21, 20, 14, 11, 13, 12, 18, 6, 3, 23]
[1, 8, 17, 24, 10, 15, 12, 13, 20, 7, 2, 21, 3, 6, 19, 22, 9, 16, 11, 14, 23, 4, 5, 18]
[1, 8, 17, 24, 10, 15, 12, 13, 20, 7, 2, 21, 3, 6, 19, 22, 14, 11, 16, 9, 23, 4, 5, 18]
[1, 8, 17, 24, 10, 15, 12, 13, 20, 7, 2, 21, 6, 3, 22, 19, 9, 16, 11, 14, 23, 4, 5, 18]
[1, 8, 17, 24, 10, 15, 12, 13, 20, 7, 2, 21, 6, 3, 22, 19, 14, 11, 16, 9, 23, 4, 5, 18]
[1, 8, 17, 24, 10, 15, 12, 13, 21, 6, 3, 20, 2, 7, 18, 23, 9, 16, 11, 14, 22, 5, 4, 19]
[1, 8, 17, 24, 10, 15, 12, 13, 21, 6, 3, 20, 2, 7, 18, 23, 14, 11, 16, 9, 22, 5, 4, 19]
[1, 8, 17, 24, 10, 15, 12, 13, 21, 6, 3, 20, 7, 2, 23, 18, 9, 16, 11, 14, 22, 5, 4, 19]
[1, 8, 17, 24, 10, 15, 12, 13, 21, 6, 3, 20, 7, 2, 23, 18, 14, 11, 16, 9, 22, 5, 4, 19]
[1, 8, 17, 24, 10, 15, 12, 13, 22, 5, 4, 19, 2, 7, 18, 23, 9, 16, 11, 14, 21, 6, 3, 20]
[1, 8, 17, 24, 10, 15, 12, 13, 22, 5, 4, 19, 2, 7, 18, 23, 14, 11, 16, 9, 21, 6, 3, 20]
[1, 8, 17, 24, 10, 15, 12, 13, 22, 5, 4, 19, 7, 2, 23, 18, 9, 16, 11, 14, 21, 6, 3, 20]
[1, 8, 17, 24, 10, 15, 12, 13, 22, 5, 4, 19, 7, 2, 23, 18, 14, 11, 16, 9, 21, 6, 3, 20]
[1, 8, 17, 24, 10, 15, 12, 13, 23, 4, 5, 18, 3, 6, 19, 22, 9, 16, 11, 14, 20, 7, 2, 21]
[1, 8, 17, 24, 10, 15, 12, 13, 23, 4, 5, 18, 3, 6, 19, 22, 14, 11, 16, 9, 20, 7, 2, 21]
[1, 8, 17, 24, 10, 15, 12, 13, 23, 4, 5, 18, 6, 3, 22, 19, 9, 16, 11, 14, 20, 7, 2, 21]
[1, 8, 17, 24, 10, 15, 12, 13, 23, 4, 5, 18, 6, 3, 22, 19, 14, 11, 16, 9, 20, 7, 2, 21]
[1, 8, 17, 24, 10, 15, 14, 11, 22, 7, 2, 19, 4, 5, 20, 21, 9, 16, 13, 12, 23, 6, 3, 18]
[1, 8, 17, 24, 10, 15, 14, 11, 22, 7, 2, 19, 4, 5, 20, 21, 12, 13, 16, 9, 23, 6, 3, 18]
[1, 8, 17, 24, 10, 15, 14, 11, 22, 7, 2, 19, 5, 4, 21, 20, 9, 16, 13, 12, 23, 6, 3, 18]
[1, 8, 17, 24, 10, 15, 14, 11, 22, 7, 2, 19, 5, 4, 21, 20, 12, 13, 16, 9, 23, 6, 3, 18]
[1, 8, 17, 24, 10, 15, 14, 11, 23, 6, 3, 18, 4, 5, 20, 21, 9, 16, 13, 12, 22, 7, 2, 19]
[1, 8, 17, 24, 10, 15, 14, 11, 23, 6, 3, 18, 4, 5, 20, 21, 12, 13, 16, 9, 22, 7, 2, 19]
[1, 8, 17, 24, 10, 15, 14, 11, 23, 6, 3, 18, 5, 4, 21, 20, 9, 16, 13, 12, 22, 7, 2, 19]
[1, 8, 17, 24, 10, 15, 14, 11, 23, 6, 3, 18, 5, 4, 21, 20, 12, 13, 16, 9, 22, 7, 2, 19]
[1, 8, 17, 24, 11, 14, 9, 16, 18, 5, 4, 23, 3, 6, 19, 22, 12, 13, 10, 15, 21, 2, 7, 20]
[1, 8, 17, 24, 11, 14, 9, 16, 18, 5, 4, 23, 3, 6, 19, 22, 15, 10, 13, 12, 21, 2, 7, 20]
[1, 8, 17, 24, 11, 14, 9, 16, 18, 5, 4, 23, 6, 3, 22, 19, 12, 13, 10, 15, 21, 2, 7, 20]
[1, 8, 17, 24, 11, 14, 9, 16, 18, 5, 4, 23, 6, 3, 22, 19, 15, 10, 13, 12, 21, 2, 7, 20]
[1, 8, 17, 24, 11, 14, 9, 16, 19, 4, 5, 22, 2, 7, 18, 23, 12, 13, 10, 15, 20, 3, 6, 21]
[1, 8, 17, 24, 11, 14, 9, 16, 19, 4, 5, 22, 2, 7, 18, 23, 15, 10, 13, 12, 20, 3, 6, 21]
[1, 8, 17, 24, 11, 14, 9, 16, 19, 4, 5, 22, 7, 2, 23, 18, 12, 13, 10, 15, 20, 3, 6, 21]
[1, 8, 17, 24, 11, 14, 9, 16, 19, 4, 5, 22, 7, 2, 23, 18, 15, 10, 13, 12, 20, 3, 6, 21]
[1, 8, 17, 24, 11, 14, 9, 16, 20, 3, 6, 21, 2, 7, 18, 23, 12, 13, 10, 15, 19, 4, 5, 22]
[1, 8, 17, 24, 11, 14, 9, 16, 20, 3, 6, 21, 2, 7, 18, 23, 15, 10, 13, 12, 19, 4, 5, 22]
[1, 8, 17, 24, 11, 14, 9, 16, 20, 3, 6, 21, 7, 2, 23, 18, 12, 13, 10, 15, 19, 4, 5, 22]
[1, 8, 17, 24, 11, 14, 9, 16, 20, 3, 6, 21, 7, 2, 23, 18, 15, 10, 13, 12, 19, 4, 5, 22]
[1, 8, 17, 24, 11, 14, 9, 16, 21, 2, 7, 20, 3, 6, 19, 22, 12, 13, 10, 15, 18, 5, 4, 23]
[1, 8, 17, 24, 11, 14, 9, 16, 21, 2, 7, 20, 3, 6, 19, 22, 15, 10, 13, 12, 18, 5, 4, 23]
[1, 8, 17, 24, 11, 14, 9, 16, 21, 2, 7, 20, 6, 3, 22, 19, 12, 13, 10, 15, 18, 5, 4, 23]
[1, 8, 17, 24, 11, 14, 9, 16, 21, 2, 7, 20, 6, 3, 22, 19, 15, 10, 13, 12, 18, 5, 4, 23]
[1, 8, 17, 24, 11, 14, 12, 13, 19, 7, 2, 22, 4, 5, 20, 21, 9, 16, 10, 15, 23, 3, 6, 18]
[1, 8, 17, 24, 11, 14, 12, 13, 19, 7, 2, 22, 4, 5, 20, 21, 15, 10, 16, 9, 23, 3, 6, 18]
[1, 8, 17, 24, 11, 14, 12, 13, 19, 7, 2, 22, 5, 4, 21, 20, 9, 16, 10, 15, 23, 3, 6, 18]
[1, 8, 17, 24, 11, 14, 12, 13, 19, 7, 2, 22, 5, 4, 21, 20, 15, 10, 16, 9, 23, 3, 6, 18]