Number grid Essay Example | Topics and Well Written Essays - 1500 words

Number grid - Essay Example Upper Left No. UL*LR UR*LL Difference 1 23 63 40 26 1248 1268 40 33 1815 1855 40 48 3360 3400 40 55 4235 4275 40 62 5208 5248 40 78 7800 7840 40 TABLE 2 As the table indicates, no matter where we place the square in the grid the difference in the product of the corners for a 3 x 3 square is always 40. Table 3 below are the results of a square that is 4 x 4 placed randomly on the grid. Upper Left No. UL*LR UR*LL Difference 1 34 124 90 17 850 940 90 24 1368 1458 90 36 2484 2574 90 41 3034 3124 90 53 4558 4648 90 67 6700 6790 90 TABLE 3 As the table indicates, no matter where we place the square in the grid the difference in the product of the corners for a 4 x 4 square is always 90. Table 4 below are the results of a square that is 5 x 5 placed randomly on the grid. Upper Left No. UL*LR UR*LL Difference 1 45 205 160 16 960 1120 160 23 1541 1701 160 35 2765 2925 160 42 3612 3772 160 56 5600 5760 160 TABLE 4 As the table indicates, no matter where we place the square in the grid the difference in the product of the corners for a 5 x 5 square is always 160. Table 5 below are the results of a square that is 6 x 6 placed randomly on the grid. Upper Left No. UL*LR UR*LL Difference 1 56 306 250 15 1050 1300 250 23 1794 2044 250 23 1794 2044 250 21 1596 1846 250 32 2784 3034 250 45 4500 4750 250 41 3936 4186 250 TABLE 5 As the table indicates, no matter where we place the square in the grid the difference in the product of the corners for a 6 x 6 square is always 250. Table 6 below are the results of a square that is 7 x 7 placed randomly on the grid. Upper...This is true for a 2 x 2 square and all other sizes. However, the difference in the product of the corners is dependent upon the size of the square. As the size of the square gets larger, the difference in the product of the corners also increases. But is there an algebraic relationship between the size of the square and the difference of the product of the corners Can we calculate the difference by knowing the size of the square Table 10 lists the results from the previous investigations. As we have seen, no matter what size square is used, we can use algebra to calculate the number of possible squares and the difference in the product of their corners. This applies to all possible combinations placed on the grid.