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Painted Cubes An Investigation by Adam Green Introduction I have a lot of 1cm cubes. These can be stuck together to make a larger cube. I paint each side of my larger cube, like this: . Then I take my new cube apart. I am left with 4 different types of cubes. Type A has 3 of its sides painted: Type B has 2 of its sides painted: Type C has 1 of its sides painted: Type D has no sides painted: i have to work out how many of each type of these cubes fit into a 3x3x3, 4x4x4 cube etc. When counted up, my results looked like this: Type A Type B Type C Type D Total 2x2x2 8 0 0 0 8 3x3x3 8 12 6 1 27 4x4x4 8 24 24 8 64 5x5x5 8 36 54 27 125 6x6x6 8 48 96 64 216 Now we have to find expressions to help us find a 10x10x10 cube Predictions I have decided to look for patterns between each of the different values to estimate the values for a 7x7x7 cube The Type A cubes appear only on the corners (vertices) of the larger cubes....

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