• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6

# Tiles investigation

Extracts from this document...

Introduction

Tim Buxton        Page         Mathematics Coursework

Investigation

‘Tiles’

A builder is asked to arrange some tiles on a wall in a 4 by 4 array as shown below

To help him he has variously shaped ‘spacers’ which he places between the tiles.

He uses the spacers to separate the tiles evenly as in the following arrangement.

He has used 4 spacers like this

He uses 9 spacers shaped like this

He uses 12 spacers shaped like this

He has 25 spacers altogether

Aim of Investigation:

The aim of this investigation is to investigate the number of different types of spacers required for other arrangements of tiles.

Result Table 1:

 Arrangement (A) C S N 1 by 1 4 0 0 2 by 2 4 1 4 3 by 3 4 4 8 4 by 4 4 9 12

By observing the results from this table after drawing the arrangements, as shown above, I have discovered a

Middle

8 by 8

4

49

28

The drawing below is drawn to express that my formulae is correct. I must state that this formula is used so that the person will not have to draw large diagrams.

Using the results from the table, I want to see if my formulae work. I decide to use the 6 by 6 arrangement as shown below,

This is what I discovered,

 Arrangement (A) C S N 6 by 6 4 25 20

By referring back to Result Table 2, I can conclude that my formulae are accurate and do work.

This can be proven below,

C = 4                 = (This is correct)

S = (A – 1) 2        = 6 – 1 = 5 = 25 (This is correct)

N = 4(A – 1)                = 6 – 1 = 5 × 4 = 20 (This is correct)

Knowing that my formulae is correct, the builder if given a square arrangement will know how many different spacers he will need, Below is a table to demonstrate this,

 Arrangement (A) C S N

Conclusion

4

6

10

I started to notice patterns. Obviously we know that (C) = 4. However (N) is increasing by 4 every time.

I carried on drawing the rectangular tile arrangement, as shown on the rough diagrams sheet.

These are the results that I discovered

 Arrangement (A) C S N 4 by 5 4 12 14 5 by 6 4 20 18 6 by 7 4 30 22 7 by 8 4 42 26

I have discovered the formula to work out S

I must state like I did earlier on in the investigation that the letter (A) represents the arrangements. However when this letter is in formulae, you must take the first number of the arrangement in order to work out.

A - A = S

However this formula only applies in certain arrangements, for example, if the first number in the arrangement is 12 it has to by 13, one added on to the first number.

Using this formula I can know how many spacers I need to fill between the tiles.

 Arrangement (A) S 8 by 9 56 32 by 33 992 128 by 129 16256 300 by 301 89700

This student written piece of work is one of many that can be found in our GCSE Sliding Puzzle section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE Sliding Puzzle essays

1. ## Maths Mayfield High School Data Handling

After my samples are selected, in any of the ways above, I will have to present the data and prove what I think is correct. This will be done by: > Aim and hypothesis - when these are made, it will provide me with something to prove.

2. ## How LCD screens work.

The capacitor is able to hold the charge until the next refresh cycle. And if we carefully control the amount of voltage supplied to a crystal, we can make it untwist only enough to allow some light through. By doing this in very exact, very small increments, LCDs can create a gray scale.

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to
improve your own work