March 2005
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Answer:
The only known way to attack this problem is to look for solutions invariant to rotations about a triagonal of the cube. It is possible to use greedy search and care only about distinct signatures of the rows. Since the cube invariant to rotations about a triagonal it will have all distinct signatures for the columns and stacks as well.
One of the solutions:
z=1: z=2: z=3: z=4: z=5: z=6:
010011 101001 111011 001111 111101 111111
001001 100111 010111 010101 011000 101101
000100 011110 100001 110011 011101 000111
000101 001011 011001 010010 100011 011111
000011 010100 001101 010110 001110 101011
000000 000001 000010 001100 010001 011011
The axled triagonal here goes from the bottom left corner of the z=1 slice to the top right corner of the z=6 slice.
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