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Introduction My investigation is to find out the number of hidden faces when x amount of cubes are placed on a table. E.g. 1 cube 6 faces 5 faces visible 1 face hidden Number Visible faces Hidden faces 1 5 1 2 8 4 3 11 7 4 14 10 5 17 13 6 20 16 7 23 29 8 26 22 9 25 29 10 28 32 It is clear from the table that there is a common pattern apparent in both the progression of visible faces and the progression of hidden faces. In fact both share the same pattern in that they both progress by 3 with each addition of a block. Finding the Nth term From this pattern and from the table I make the formula for the progression of visible faces: 3n + 2 e.g. Number of cubes = 2 Number of visible faces = 2 2 x 3 = 6 + 2 = 8 = 3n + 2 I have proved that this formula works by calculating the 9th and 10th terms by using it. From the pattern and from...

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