*So I then went on to investigate the same step size on another different size of grid, this time a 6 x 6 size grid.Here is what I found: When I investigated the different sized grid I noticed that each different grid size gave the stair total a different formula because each time a different number was added.*

Lastly I went on to learn about the fifth and final stair size; the five step stair.

Once again here are the results: X x 1 x 2 x 3 x 4 x g x g 1 x g 2 x g 3 x g g x g g 1 x g g 2 x g g g x g g g 1 x g g g g = 15x 20g 20 On all of the grids on which I tested this I found that this was constantly the formula.

Also I have found out that the size of the corner number does not affect the amount that ‘g’ is multiplied nor does it affect the number that is added on the end of the formula.

Also I have found out that the value of ‘g’ is different in each grid depending on the size of the grid.

After finding the totals for each of the stairs that I will use I shall work out the formula by using the same method as before.

Here is what I found out: X x 1 x 2 x 3 x g x g 1 x g 2 x g g x g g 1 x g g g = 10x 10g 10 Looking at the above information it is visible to know that the four step stair shape follows the same simple pattern as the three step stairs in the way that the letter g is added vertically and the numbers added horizontally.It is easy to work out because there is six ‘x’s then you have to times x by 6 then you just add the other numbers together to get 44. Lastly I have noticed that this formula does in fact work for any stairs anywhere in this number grid. It is evident that the larger the corner number is the larger the stair total is going to be.The reason for this is that the higher ‘x’ is then the more it is multiplied.First of all I decided to investigate using the same size steps on an 8 x 8 number grid.Here is what I found out: x x 1 x 2 x 8 x 9 x 16 = 6x 36 Therefore as you can see above the formulas for the three step stairs on different sized number grids do not seem to be exactly the same (other than each time the multiplication of ‘x’ has been the same).Now that I have experimented with three different grids but with the same size of steps I have also noticed that the number that is always added vertically is always the number that is the same size of the grid.So for example for a 10 x 10 grid as the numbers increase upward from the corner number each time it is increased by ten.So for the three step total on any size grid the formula is; 6x 4g 4 Different Stair Sizes Next I shall investigate different stair sizes and the formulas for their totals.The first grid size I will choose to use is 10 x 10 and the size stairs will be a four step size.In this investigation it has also been proved that wherever the stairs are in the grid the formula for their total still applies.Part 2 – Other Steps on Other Number Grids Now that I have finished the three step stair on just a 10 x10 number grid I shall go on to changing first the grid size and then the steps size.

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