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Hidden faces

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Introduction

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. ...read more.

Middle

From the pattern and from the table I make the formula for the progression of hidden faces: 3n - 2 e.g. Number of cubes = 2 Number of hidden faces = 4 2 x 3 = 6 - 2 = 4 = 3n - 2 I have proved that this formula works by finding the 9th and 10th terms by using it. Alternative method An alternative way of working out the hidden number of hidden faces is to gather the number of visible faces and subtract that number from the original amount of faces. ...read more.

Conclusion

Finding the Nth term From the pattern and from the table I make the formula for the progression of visible faces: 6n + 4 e.g. Cube number = 2 Number of visible faces = 26 6 x 2 = 12 + 14 = 26 = 6n + 4 I have proved that this works by using it to calculate the 5th and 6th terms. From the pattern and the table I make the formula for the progression of hidden faces: 18n + 10 e.g. Cube number = 2 Number of hidden faces = 46 18 x 2 = 36 + 10 = 46 = 18n + 10 I have proved that this works by using it to calculate the 5th and 6th terms. ...read more.

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