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Investigating Number Stairs  

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Maths Coursework(c) - Investigating Number Stairs Part 1 46 36 37 26 27 28 To investigate the relationship of other 3-step stairs, their stair total and their position on the grid, we can move it one space to the right. We then get the following in the 10x10grid: 26+27+28+36+37+46=200 Therefore total = 200 If we continue moving the shape to the right, and continue this for each row on the grid, we get a pattern like this: 1 2 3 4 5 194 200 206 212 218 S+20 S+10 S+11 S S+1 S+2 We can say that it increases in a linear fashion (the increase is constant). To use a formula to find out the stair total every time, we can make use of the bottom left had corner of the stair and change it to S. Every other number can be changed so that it is related to S So the total for any 3-step stair on the 10x10 grid= 6S+44 We can test this formula for the very first grid we did: (6x25) + (44) = 194...

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