1.25

The interesting matrix that is formed by this (iteration) output versus input with 9 problems is not only linear but also:

 

 

Input:

9

8

7

6

5

4

3

2

1

0

 

Output:

8

7

6

5

4

3

2

1

0

?

Difference:

 

11

11

11

11

11

11

11

11

?

Or:

98

87

76

65

54

43

32

21

10

?

 

Time input:

0

1

2

3

4

5

6

7

8

9

Output:

9

8

7

6

5

4

3

2

1

0

Sum:

0 + 9 = 9

1 + 8 = 9

2 + 7 = 9

3 + 6 = 9

4 + 5 = 9

5 + 4 = 9

6 + 3 = 9

7 + 2 = 9

8 + 1 = 9

9 + 0 = 9

Or:

09

18

27

36

45

54

63

72

81

90

Difference:

 

9

9

9

9

9

9

9

9

9

If we look at input and output we not only see nice products but also in multiplication the sequence of 1 x 9, 2 x 9, 3 x 9 etc, resulting in 9, 18, 27, 36 etc, is formed automatically. But also the combination of input and output resulting in a difference of constant 11 will play a major role in my story.

 

While working from the start with the number 9, I was wondering if other numbers would give the same result. After all kind of trials I started with this matrix at the upper right corner: input 0, output 9, input 1being 9 – output 8, input 2 being 8 – output 7, etc. Output becomes input and so on.

Surprisingly one will get  a normal  1, 2, 3, 4 …90 counting sequence. Of course you will find some numbers are missing. 

 

be patient

1.25 will come 

to life!

 

In the next picture the whole matrix is shown, plus an additional 9 numbers adding up to 99.

A diagonal line starting in any point of the matrix will find its anti pole right through the centre point 50 and the product of the both of them will always be 100. Every point in itself will have the same relation to its surrounding points as the 50 does. 

Example: 2 x 50 = 100 the product of all the diagonal endpoints that have 50 as their centre. This counts for every point.

 

Recall the differences 9 and 11, it now is  a rectangle 9 by 11