How many ways are there to stack a plain cube or a die?
How many ways are there to stack two plain cubes or two different coloured dice?
How many ways are there to stack three plain cubes or three different coloured dice?
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How many ways are there to stack a plain cube or a die?
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How many ways are there to stack two plain cubes or two different coloured dice?
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How many ways are there to stack three plain cubes or three different coloured dice?
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How many ways can you stack 4, 5, 6 or n identical cubes? Find the surface area of the two stacking arrangements that are possible for three identical cubes. Draw out the stacking arrangements for 4 and 5 identical cubes and calculate their surface areas. Can you find a formula for the maximum surface area of a stack of n cubes? Can you find a formula for the edge dimension of the minimum surface area stack for a stack of n cubes? Repeat this exercise using squares on a plane surface. What is the formula for the edge of the minimum perimeter arrangement for n squares? Repeat this exercise using squares on a single line. What is the formula for the maximum and minimum length for n squares? Repeat this exercise using N dimensions. What is the formula for the edge dimension for minimum value of the analogue of "surface area" for a stack of n N-dimensional cubes? |