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February 9th, 2015, 06:17 AM   #1
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16 of the 64 unit cubes are painted red on all faces. The 64 unit cubes are then arranged into a 4x4x4 cube. How many arrangements exist such that for every 1x1x4 cube inside the 4x4x4 cube, there is exactly one red cube?
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February 9th, 2015, 06:50 AM   #2
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For an arrangement of red cubes to work for all ways of forming 1x1x4 pieces, no red cube can share a row, column or 'pillar' with another red piece.
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February 9th, 2015, 01:21 PM   #3
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Though "1 by 1 by 4" would not be a "cube".
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