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# Investigate the number of hidden faces when cubes are joined indifferent ways.

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Introduction

### Hidden Faces Investigation: Investigate the number of hidden faces when cubes are joined in different ways

Andrew Bambridge 10FA3 Hidden Faces Coursework

I am going to investigate the number of hidden faces when cubes are joined in different ways. The aim of this task is to find a formula which is common with every cube and hidden face.

In order for me to find the overall formula which ca be found by finding out a formula which can determine the outcome of number of hidden faces on ‘n’ cubes. I will have to start by spotting patterns and their differences then find out how each set of hidden faces are common with each other.

Middle

There are 33 hidden faces and 21 seen faces

There are 46 hidden faces and 26 seen faces

There are 59 hidden faces and 31 seen faces

I predict that the next set of results will be 72 hidden faces and 36 seen faces

There are 72 hidden faces and 36 seen faces

Results

Difference: There is a difference of 13 between the hidden faces

There is a difference of 5 between the seen faces

There are 10 hidden faces and 14 seen faces

There are 28 hidden faces and 20 seen faces wwge gewstgegeud ege gentcge engetral gecoge uk.

There are 46 hidden faces and 26 seen faces

I predict that the next number of hidden faces will be 64 and there will be 32 seen faces

Because of my rule of 18n-8

There are 64 hidden faces and 26 seen faces

Results

There are 16 hidden faces and 20 seen faces from www.studentcentral.co.uk

There are 44 hidden faces and 28 seen faces

Conclusion

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wweg egwstegegud eeg egntceg enegtral egcoeg uk.

There are 100 hidden faces and 44 seen faces

I predict that the next set of results will be 128 hidden faces and 52 seen faces

wwdd ddwstddddud edd ddntcdd enddtral ddcodd uk!

There are 128 hidden faces and 52 seen faces

wwbe bewstbebeud ebe bentcbe enbetral becobe uk.

Results

There are 10 hidden faces and 14 seen faces

There are 28 hidden faces and 20 seen faces

There are 46 hidden faces and 26 seen faces

8i9DsVhZ from 8i9DsVhZ student 8i9DsVhZ central 8i9DsVhZ co 8i9DsVhZ uk

There are 64 hidden faces 32 seen faces

Results

Formula

I have come to the conclusion that this formula will work with most hidden faces wwcg cgwstcgcgud ecg cgntccg encgtral cgcocg uk.

## L[(5r-2)n-2r]

To prove this works I have tested this theory.

Eg. Take a 3x6

1[(5x3-2)6-2x3]

This student written piece of work is one of many that can be found in our GCSE Hidden Faces and Cubes section.

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