*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.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.

Therefore I have found out that that the formula for steps of this size is; 10x 10g 10.

Next I shall attempt to find out about a one step stair.

I have shown this below representing the grid size by using the letter ‘g’.

x x 1 x 2 x g x g 1 x g g = 6x 4g 4 After checking this formula to see if it works for each size of grid it has been proven that it does work.

Although the corner number affects the multiplication of x, it does not affect the number 4 which always remains the same no matter what the corner number is.

So, the three step stairs could be located anywhere in the grid and the only part of the formula that will change is the amount of times that you multiply x.Below is an example of just one of the three sets of stairs that I used to conduct my investigation: I have worked out the formula for the total inside the three step stairs in a 10 x 10 grid Key: x = corner number t = total inside stairs 1.I worked out the common relationship with the numbers inside the stairs and to be accurate here are two examples: x x 1 x 2 x 10 x 11 x 20 = 6x 44 2.Part 1- Three Step grid I have investigated the three step stair (some of my findings can be viewed on the graph paper in the back).During my investigation I believe that I have worked out the formula for the total inside the three step stairs on a 10 x 10 grid.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.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.Noticing that this is the total I realised that it is not so hard to work out the formula for the total.Therefore due to the above diagram it is evident that the formula must be, 6x 44.

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