Compact Plus 16x16 Magic Square
Connection
of the Sub-Squares
The large square is divided into 16 sub-squares of 4 x 4.
Each sub-square is connected to all the others, both horizontally and
vertically.
With the help of the key values, these sub-squares can be mirrored.
Key Values
Key values are the sum of two numbers from the square and always consist of two
values. Together, they ultimately connect all numbers with each other.
Because each key value consists of two pairs, this involves a total of four
numbers.
The average value of four numbers in a 16 x 16 square is always 514 (the magic
sum 2056 divided by 4).
The key values are calculated using a calculation
value, which depends on the size of the magic square.
In this example, the square is 16 x 16:
16 x 16 = 256.
The value 256 represents the difference between two numbers that together add
up to 514.
The first key values that arise from this are: 129 and 385 (together 514).
Calculation Values
The first calculation value is 256.
After that, this value is repeatedly divided by 2, which gives the following
sequence:
256 – 128 – 64 – 32 – 16 – 8 – 4 – 2
These calculation values lead to the following key
values:
- 256 → 129 – 385
- 128 → 193 – 321
- 64 → 225 – 289
- 32 → 241 – 273
- 16 → 249 – 265
- 8 → 253 – 261
- 4 → 255 – 259
- 2 → 256 – 258
Use of the Key Values
The key values can be applied in different orders.
Depending on the chosen order, a different magic square will be created each
time.
In the attached example, a different order has been used.
Connection of the Sub-Squares
Horizontal
Sub-square 1 and 2 are connected by the key values 253-261.
As well as block 3 and 4.
Sub- square 1 and 3 are connected by the key values 225-289.
As well as block 2 and 4.
Sub- square 1 and 4 are connected by the key values 129-385.
As well as block 2 and 3.
Vertical
Sub-square 1 and 2 are connected by the key values 249-265.
As well as block 3 and 4.
Sub- square 1 and 3 are connected by the key values 241-273.
As well as block 2 and 4.
Sub- square 1 and 4 are connected by the key values 193-321.
As well as block 2 and 3.
Constructing the first 2x2 square.
The starting point is always the number 1. Here at
first position.
Generating the horizontal number by the key values
256-258. In this case 256.
Which gives the number 255 = 256-1.
Generating the vertical number by the key values 255-259.
In this case 255.
Which gives the number 254 = 255-1.
The last number can the generated horizontal of
vertical.
258-254= 4 or 259-255= 4
|
1 |
255 |
|
254 |
4 |
