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Exposed cube sides
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| Submitted: Tue Mar 29 2005
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Introduction In this investigation I will be finding out how many labels are on an exposed side of a 3x3x3 cube when 27 small cubes are put together to make the large 3x3x3 cube. Method I will first start to count the number of small cubes out of the 27; have no labels, 1 label, 2 labels and 3 labels. Once I have done this I will the do the same for a 4x4x4 cube, 5x5x5 cube and finally a 6x6x6 cube and see if I can find a pattern. When I have found a pattern I will try to work out a formula and test if it works. 4x4x4 3x3x3 Key 3 labels 2 labels 1 label No labels 6x6x6 5x5x5 Results 3x3x3 4x4x4 5x5x5 6x6x6 3 labels 8 8 8 8 2 labels 12 24 36 48 1 labels 6 24 54 96 No labels 1 8 27 64 Formula The pattern for 3 labels is 8, 8, 8... U3 = 8 = 0x3+8 U4...
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