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3 by 3 step stair

Extracts from this document...

Introduction

Andrew Belcher

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This is a 3 by 3 step stair, this is because the step stair goes up by three squares and down by three squares. We will call this step stair ‘S-number 1’ as that is the number in the bottom left of the step stair. The step stair total (which we will call the S-total) is all the numbers within the step stair added together. The step stair total for this step stair for example is 50, as 1+2+3+11+12+21=50

I am now going to try and find an algebraic equation for finding the S-total from the S-number. I am now going to find a link between the S-number (which we will call N) and the rest of the numbers in the grid:

N+20

...read more.

Middle

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In this example the S-total is 14, as 1+2+11=14. I am now going to find how the S-number links with the rest of the numbers in the step stair (we will call the S-number N).

N+10

N        N+1

I am going to find the general rule as I did previously:

This will give me 3N+11.

I can prove this by using the example S-number 1. Using the rule the S-total comes to 14, by adding all of the numbers within the step stair it also comes to 14. Therefore the rule works.

I can prove this again by using the S-number 2.

...read more.

Conclusion

N+30  

N+20  N+21

N+10  N+11  N+12

N        N+1    N+2    N+3

Using the previous method I can determine that the rule is

10N+110

I can prove this by using the first example. Using the rule the S-total is 120, adding all the numbers within the step stair also gives you 120. So the rule works.

I am now going to find a relationship between grid size and the S-total. I am going to use a standard 3x3 grid.

11x11 Grid

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I am going to find the rule like I have done in the previous exercises for several grid sizes. I am now going to draw a table of my results:

Grid size

Rule

9x9

6N+41

10x10

6N+44

11x11

6N+48

...read more.

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

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