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