I have found that they all end out that the difference between the two numbers of any 2 x 2 squares on a 1 – 100 grid is 10.
Algebra - 2 x 2
(X2 + 10X +1X +10) - (X2 + 11X)
FORMULA = (X2 + 11X +10) – (X2 +11X) = 10
3 x 3 Squares
My 3 x 3 square is 42, 43, 44, 52, 53, 54, 62, 63 and 64. The top left times by the bottom right is 42 x 64 =2688. The top right multiplied by the bottom left is44 x 62 = 2728. The difference between the smaller and bigger numbers is 2728 – 2688 = 40.
My 3 x 3 square is 1, 2, 3, 11, 12, 13, 21, 22 and 23. The top left times by the bottom right is 1 x 23 = 23. The top right multiplied by the bottom left is 3 x 21 = 63. The difference between the smaller and bigger numbers is 63 – 23 = 40.
My 3 x 3 square is 17, 18, 19, 27, 28, 29, 37, 38 and 39. The top left times by the bottom right is 17 x 39 = 663. The top right multiplied by the bottom left is 19 x 37 = 703. The difference between the smaller and bigger numbers is 703 – 663 = 40.
My 3 x 3 square is 78, 79, 80, 87, 88, 89, 90, 98, 99 and 100. The top left times by the bottom right is 78 x 100 = 7800. The top right multiplied by the bottom left is 80 x 98 = 7840. The difference between the smaller and bigger numbers is 7840 – 7800 = 40.
I have found that they all end out that the difference between the two numbers of any 3 x 3 squares on a 1 – 100 grid is 40.
Algebra – 3 x 3
(X2 + 2X + 20X + 40) – (X2 +22X) = 40
FORMULA = (X2 + 22X + 40) - (X2 +22X) = 40
4 x 4 Squares
My 4 x 4 square is 17, 18, 19, 20, 27, 28, 29, 30, 37, 38, 39, 40, 47, 48, 49 and 50. The top left times by the bottom right is 17 x 50 = 850. The top right multiplied by the bottom left is 20 x 47 = 940. The difference between the smaller and bigger numbers is 940 – 850 = 90.
My 4 x 4 square is 1, 2, 3, 4, 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33 and 34. The top left times by the bottom right is 1 x 34 = 34. The top right multiplied by the bottom left is 4 x 31 = 124. The difference between the smaller and bigger numbers is 124 – 34 = 90.
My 4 x 4 square is 62, 63, 64, 65, 72, 73, 74, 75, 82, 83, 84, 85, 92, 93, 94 and 95. The top left times by the bottom right is 62 x 95 = 5890. The top right multiplied by the bottom left is 65 x 92 = 5980. The difference between the smaller and bigger numbers is 5980 – 5890 = 90.
My 4 x 4 square is67, 68, 69, 70, 77, 78, 79, 80,87, 88, 89, 90, 97, 98, 99 and 100. The top left times by the bottom right is 67 x 100 = 6700. The top right multiplied by the bottom left is 70 x 97 = 6790. The difference between the smaller and bigger numbers is 6790 – 6700 =90.
I have found that for any 4 x 4 square on a 1-100 grid the difference between the two numbers is 90.
Algebra – 4 x 4
(X2 + 3X + 30X + 90) – (X2 + 33X) = 90
FORMULA = (X2 + 33X + 90) – (X2 + 33X) = 90
5 x 5 Squares
My 5 x 5 square is 1, 2, 3, 4, 5, 11, 12, 13, 14, 15, 21, 22, 23, 24, 25, 31, 32, 33, 34, 35, 41, 42, 43, 44 and 45. The top left times by the bottom right is 1 x 45 = 45. The top right multiplied by the bottom left is 5 x 41 = 205. The difference between the smaller and bigger numbers is 205 – 45 = 160.
My 5 x 5 square is 6, 7, 8, 9, 10, 16, 17, 18, 19, 20, 26, 27, 28, 29, 30, 36, 37, 38, 39, 40, 46, 47, 48, 49 and 50 The top left times by the bottom right is 6 x 50 =300. The top right multiplied by the bottom left is 10 x 46 = 460. The difference between the smaller and bigger numbers is 460 – 300 = 160.
My 5 x 5 square is 51, 52, 53, 54, 55, 61, 62, 63, 64, 65, 71, 72, 73, 74, 75, 81, 82, 83, 84, 85, 91, 92, 93, 94 and 95. The top left times by the bottom right is 51 x 95 = 4845. The top right multiplied by the bottom left is 55 x 91 = 5005. The difference between the smaller and bigger numbers is 5005 – 4845 = 160.
My 5 x 5 square is 56, 57, 58, 59, 60, 66, 67, 68, 69, 70, 76, 77, 78, 79, 80, 86, 87, 88, 89, 90, 96, 97, 98, 99 and 100. The top left times by the bottom right is 56 x 100 = 5600. The top right multiplied by the bottom left is96 x 60 = 5760. The difference between the smaller and bigger numbers is 5760 – 5600 = 160.
I have found that they all end out that the difference between the two numbers of any 5 x 5 squares on a 1 – 100 grid is 160.
Algebra - 5 x 5
(X2 + 40X + 4X + 160) – (X2 + 44X) = 160
FORMULA = (X2 + 44X + 160) – (X2 + 44X) = 160
Algebra for All
The algebra for all the equations is 10(n-1)2. This formula can be used to find out any size square on a 10 x 10 grid.
