T-total coursework
Part 1 Investigate the relationship between the T-total and the T-number 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 2 3 0 1 2 9 20 21 The T-number is always the number at the bottom of the T, so in this case (the yellow T) it is 20. The sum of all the numbers in the T is the T-total. In this case, the T-number, (which will now be called n) is 20, and the T-total, (which will now be called T) is 37. If the number at the bottom of the T is n, these are the other numbers in terms of n, bearing in mind that the width of the grid is 9 (by 9): n-19 n-18 n-17 0 n-9 2 9 n 21 The number above the T-number is (n-9) because this number is exactly one row above (n). The width of the grid is 9, so by moving up 1 cell from (n), I am decreasing the value by the width of the grid (9). The cell above (n-9) is (n-18) as the value has been decreased by the width of the grid again. The cell to the left of (n-18) is (n-19) as it has been decreased by 1. The cell to the right of (n-18) is (n-17) as it is 1 more than (n-18). When these 5 terms are added together I get: (n) + (n-9) + (n-17) + (n-18) + (n-19) = 5n - 63
T-TOTALS
Mathematics Coursework: T-Totals T-Totals - 10x10 Grid 1+2+3+12+22= 40 T-Number=22 T-Total= 40 24+25+26+35+45= 145 T-Number=45 T-Total=145 61+62+63+72+82= 340 T-Number=82 T-Total=340 78+79+80+89+99= 425 T-Number=99 T-Total=425 For 10x10 Grid: * When the T-number is even, so is the T-Total. * When the T-number is odd, so is the T-Total. I will now find the rule which links the T-Number with the T-Total: n+(n-10)+(n-20)+ (n-21)+(n-19) =5n-70 When n= 59 =(5x59)-70=225 Testing: 38+39+40+49+59=225 As you can see my rule has worked. 9x9 Grid: 1+2+3+11+20= 37 T-Number=20 T-Total= 37 22+23+24+32+41= 142 T-Number=41 T-Total=142 46+47+48+56+65= 262 T-Number=65 T-Total=262 61+62+63+71+80=337 T-Number=80 T-Total=337 For 9x9 Grid: * When the T-Number is even, the T-Total is odd. * When the T-Number is odd, the T-Total is even. I will now find a rule which links the T-number with the T-Total: n+(n-9)+(n-18)+ (n-18)+(n-19) =5n-63 When n=44 =(5x44)-63=157 Testing 25+26+27+35+44=157 8x8 Grid 1+2+3+10+18= 34 T-Number=18 T-Total=34 20+21+22+29+37= 129 T-Number=37 T-Total=129 33+34+35+42+50= 194 T-Number= 50 T-Total= 194 45+46+47+54+62= 254 T-Number= 62 T-Total= 254 For 8x8 Grid: * When the T-Number is odd, the T-Total is odd. * When the T-Number is even, the T-Total is even. I will now find a rule which