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Maths Grid Coursework

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Introduction

I will now investigate different size grids. An 11 by 11 1 2 3 n=24 12 13 14 23 24 25 T=n+ (n-11) + (n-23) + (n-22) + (n-21) T=5n-77 Now test this: 24 25 26 n=47 35 36 37 T=5n - 77 46 47 48 T= (5 x 47) - 77 T=158 Check 24+25+26+36+47 =158 So this formula does work. A 6x6 grid 1 2 3 n=14 7 8 9 13 14 15 T=0 + (n-6) + (n-12) + (n-13) + (n -11) T=5n-42 Now to test it. ...read more.

Middle

(With the same amount of numbers in side the T shape) The numbers which are underlined are all divisible by 7. This means that if you know the grid size you can multiply it by 7 and it would give you the number that you would subtract from the Tnumber. From this we can make a general formula for any size grid and any Tnumber. g=grid size The General Formula is: T=5n-7g N.B This formula only applies to a T this way up: Formulae Formula Shape of 'T' 1)T=5n-3 T(in 9 by 9 grid) ...read more.

Conclusion

Therefore I think that the formula is: T=5n+7g on any grid size. Test on 9 By 9 1 2 3 T= (5x2) + (7x9) 10 11 12 T= 10+63 19 20 21 T= 73 Check 2+11+20+19+21=73 This means that this formula is correct; I will do 1 more test just to make sure. Test on 5 by 5 7 8 9 T= (5x8) + (7x5) 12 13 14 T= 40+35 17 18 19 T=75 Check 8+13+17+18+19=75 I now believe that the formula is: T=5n+7g works for an upside down T anywhere on a grid of any size. I will now investigate a T like this: ...read more.

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