The purpose of this coursework is to find the different between the products of the number in the opposite corners of each rectangle in the grid.

The difference number of 3*4

61 * 84 = 5124

 81 * 64 = 5184

5124 – 5184 = 60

The difference number of 3*5

41 * 65 = 2665

61 * 45 = 2745

2665 – 2745 = 80

The difference number of 3*6

34 * 59 = 2006

54 * 39 = 2106

2006 – 2106 = 100

Results:

3 * 3 = 40

3 * 4 = 60

3 * 5 = 80

3 * 6 = 100

20n – 20

20 (n – 1)

Test my formula for 3*7(n=7)

When width = 4:

The difference numbers of 4 * 4

31 * 64 = 1984

61 * 34 = 2074

1984 – 2074 = 90

The difference number of 4*5

61 * 95 = 5795

91 * 65 = 5915

5795 – 5975 = 120

The difference numbers of 4*6

63 * 98 = 6194

93 * 68 = 6324

6324 – 6194 = 150

Results:

4 * 4 = 90

4 * 5 = 120

4 * 6 = 150

30n  - 30

30 ( n – 1 )

Test my formula for 4 * 7 ( n = 7 )

When width = 5:

The difference number of 5 * 5

2 * 46 = 92

42 * 6 = 252

252 – 92 = 160

12 * 57 = 684

52 * 17 = 884

884 – 684 = 200

Results:

5 * 5 = 160

5 * 6 = 200

40n – 40

1 ( n – 1 )

Test my formula for 5 * 7 ( n = 7 )

        

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1.

2 * 3 = 20

2 * 4 = 30

2 * 5 = 40

2 * 6 = 50

 = 10n – 10

10 ( n - 1 )

2.

3 * 3 = 40

3 * 4 = 60

3 * 5 = 80

3 * 6 = 100

 20n – 20

20 ( n – 1 )

3.

4 * 4 = 90

4 * 5 = 120

4 * 6 = 150

30n – 30

30 ( n – 1)

4.

5 * 5 = 160

5 * 6 = 200

40n – 40

40 ( n – 1 )

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10 ( n – 1  )

20 ( n – 1 )

30 ( n – 1 )

40 ( n – 1 )

10n + 20n – 20 + 30n – 30  + 40n – 40=

= 100n – 90

2 ( 50n – 45 )

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• There is drawn round 6 numbers
• If I want to find the grid of each number
• First I need to add one x then I have to cut one number from original numbers
• then I need to multiply first break to next break take a look at it

    The difference numbers of 2 * 3

(x + 44 ) ( x + 56 )

=x ( x + 56 ) + 44 ( x + 56 )

= x2 + 56x + 44x + 2464

= x2 + 100x + 2464

Next

(x + 54 ) ( x + 46 )

=x ( x + 46 ) + 54 ( x + 46 )

= x2 + 46x + 54x + 2484

= x2 + 100x + 2484

 

This is first technique to find out the difference of the

                                2484 – 2464 = 20

          The difference numbers of 2*4

(x + 40 ) ( x + 53 )

=x ( x + 53 ) + 40 ( x + 53 )

= x2 + 53x + 40x + 2120

= x2 + 93x + 2120

Next

(x + 50 ) ( x + 43 )

=x ( x + 43 ) + 50 ( x + 43 )

= x2 + 43x + 50x + 2150

= x2 + 93x + 2150

2150 – 2120 = 30

The difference number of 2*5

(x + 70 ) ( x + 84 )

=x ( x + 84 ) + 70 ( x + 84 )

= x2 + 84x + 70x + 5880

= x2 + 154x + 5880

Next

(x + 80 ) ( x + 74 )

=x ( x + 74 ) + 80 ( x + 74 )

= x2 + 74x + 80x + 5920

= x2 + 154x + 5920

5920 – 5880 = 40

The difference number of 2*6

(x + 74 ) ( x + 89 )

=x ( x + 89 ) + 74 ( x + 89 )

= x2 + 89x + 74x + 6586

= x2 + 163x + 6586

Next

(x + 84 ) ( x + 79 )

=x ( x + 79 ) + 84 ( x + 79 )

= x2 + 79x + 84x + 6636

= x2 + 163x + 6636

6636 – 6586 = 50

The difference number of 3 * 3

(x + 4 ) ( x + 26 )

=x ( x + 26 ) + 4 ( x + 26 )

= x2 + 26x + 4x + 104

= x2 + 30x + 104

Next

(x + 24 ) ( x + 6 )

=x ( x + 6 ) + 24 ( x + 6 )

= x2 + 6x + 24x + 144

= x2 + 30x + 144

144 – 104 = 40

The difference number of 3*4

(x + 60 ) ( x + 83 )

=x ( x + 83 ) + 60 ( x + 83 )

= x2 + 83x + 60x + 4980

= x2 + 143x + 4980

Next

(x + 80 ) ( x + 63 )

=x ( x + 63 ) + 80 ( x + 63 )

= x2 + 63x + 80x + 5040

= x2 + 143x + 5040

5040 – 4980 = 60

The difference number of 3*5

(x + 40 ) ( x + 64 )

=x ( x + 64 ) + 40 ( x + 64 )

= x2 + 64x + 40x + 2560

= x2 + 104x + 2560

Next

(x + 60 ) ( x + 44 )

=x ( x + 44 ) + 60 ( x + 44 )

= x2 + 44x + 60x + 2640

= x2 + 104x + 2640

2640 – 2560 = 80

The difference number of 3*6

(x + 33 ) ( x + 58 )

=x ( x + 58 ) + 33 ( x + 58 )

= x2 + 58x + 33x + 1914

= x2 + 91x + 1914

Next

(x + 53 ) ( x + 38 )

=x ( x + 38 ) + 53 ( x + 38 )

= x2 + 38x + 53x + 2014

= x2 + 91x + 2014

2014 – 1914 = 100

The difference numbers of 4 * 4

(x + 30 ) ( x + 63 )

=X ( x + 63 ) + 30 ( x + 63 )

= X 2 + 63x + 30x + 1890

= X 2 + 93x + 1890

Next

(x + 60 ) ( x + 33 )

=x ( x + 33 ) + 60 ( x + 33 )

= x2 + 33x + 60x + 1980

= x2 + 93x + 1980

1980 – 1890 = 90

The difference number of 4*5

(x + 60 ) ( x + 94 )

=X ( x + 94 ) + 60 ( x + 94 )

= X 2 + 94x + 60x + 5640

= X 2 + 154x + 5640

Next

(x + 90 ) ( x + 64 )

=X ( x + 64 ) + 90 ( x + 64 )

= X 2 +  64x + 90x + 5760

= X 2 + 154x + 5760

5760 – 5640 = 120

The difference numbers of 4*6

(x + 62 ) ( x + 97 )

=X ( x + 97 ) + 62 ( x + 97 )

= X 2 + 97x + 62x + 6014

= X 2 +159x + 6014

Next

(x + 92 ) ( x + 67 )

=X ( x + 67 ) + 92 ( x + 67 )

= X 2 + 67x + 92x + 6164

= X 2 + 159x + 6164

6164 – 6014 = 150

The difference number of 5 * 5

(x + 1 ) ( x + 45 )

=X ( x + 45 ) + 1 ( x + 45 )

= X 2 + 45x + x + 45

= X 2 + 46x + 45

Next

(x + 41 ) ( x + 5 )

=X ( x + 5 ) + 41 ( x + 5 )

= X 2 + 5x + 41x + 205

= X 2 + 46x + 205

205 – 45 = 160

The difference number of 5 * 6

(x + 11 ) ( x + 56 )

=X ( x + 56 ) + 11 ( x + 56 )

= X 2 + 56x + 11x + 616

= X 2 + 67x + 616

Next

(x + 51 ) ( x + 16 )

=X ( x + 16 ) + 51 ( x + 16 )

= X 2 + 16x + 51x + 816

= X 2 + 67x + 816

816 – 616 = 200

 

Summarize of all the girding numbers

2 * 3 TO  2 * 6

3 * 3  To 3 * 6

4*4 To 4* 6

5 * 5 To 5 * 6