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

 

Labyrinth

A magic square with in de centre the lowest numbers 1 -256.
The numbers are organised from 256 till 1. It follows a path like al labyrint with 1 as the middle.

The square is magic because the sum of the numers in each row, column and all diagonals are the same: 131104

Here below only the center

Franklin in a magic square

The square is magic because the sum of the numbers in each row, column and all diagonals are the same: 131104

This 128x128 magic square is divided in 16 area.

The lowest of highest number in each area is white and and the opposite full colored. The other numbers are ordered in between, so slowly it goes from white to the specific color. 

And this is the result

Einstein 2

The square is magic because the sum of the numbers in each row, column and all diagonals are the same: 131104

This 128x128 magic square is divided in 16 area.

The lowest of highest number in each area is white and and the opposite full colored. The other numbers are ordered in between, so slowly it goes from white to the specific color. 

And this is the result

Einstein

The square is magic because the sum of the numbers in each row, column and all diagonals are the same: 131104

I like the experiment!
In this 128x128 magic square the lowest numbers 1-1024 are in the centre.
This numbers are coded in grayscale.
Number 1 is white and number 1014 is black. The other numbers are ordered in between, so slowly it goes from white to black. How bigger the number the more black.

And this is the result

A very special Magic Square

A magic square with in de centre the lowest numbers 1 -256.

The numbers are organised so that 1-4 are in the centre. 

Around there is a layer from the numbers 5 -16.

In the next layer around the numbers 17-36

And so on:

37-64

65-100

etc and the last (outside) layer 193-256

The square is magic because the sum of the numbers in each row, column and all diagonals are the same: 131104

The extra in this square is that in this centre the 2 by 2 squares are connected
The sum of the middle 2x2 square: 10
1+2+3+4
The sum 2x2 squares of the layer around is 34
16+7+10+1 and 8+15+2+9 and 12+3+14+5 and 4+11+6+13
The sum of de 2x2 squares in the layer around is 82
25+18+23+16 and33+34+7+8 and 17+26+15+24 and 9+30+11+32 etc
in the next layers the sum of the 2x2 squares are:
162 - 274 - 418 - 594 and 802

The centre with the layers

and the total 64x64 square

The Tilburg T in a magical square.

The square is magic because the sum of the numbers in all rows, columns and diagonals is the same, namely 131104.

In each sub-square, the T is formed by either the lowest or the highest consecutive numbers in that series and the remainder of the sub-square just the highest or lowest numbers in the same series.

E.g. the two light blue squares:
- in the upper left square, the T starts with the number 1 and ends with 68
- in the square, slightly off center in the lower right, the T starts with 4096 and ends with 4029

Note that the sum of the 2 numbers at the top left in both sub-squares is 4097. This also applies to the
numbers that are placed in the 2nd to 256th places (bottom right in the sub-square). All numbers are linked!

This applies to every part square with the same color.

The square is somewhat stretched, because the logo of the Tilburg T has a ratio of 6:7.

A spiral in the magic square

After experimenting a bit I managed to make a spiral in de centre of the magic square.

First I made a 16x16 square with the smallest numbers (1-16) in the centre.

Then I found a way to manipulate the order of this numbers.

And from this a got this idee of making a spiral where numbers are places from 1 till 16.

However a spiral of only 16 numbers is not so interesting, so I tryed with the numbers 1-64 in a 32x32 square.

And see here the result.

The square is magic at its rows, column an head-diagonals.

Which numbers are missing?

Do you know the Answer?

A new magic Square: 3 in 1 !

Did I invent a new magic square?
It is special at least.

I made a 64 x 64 square.
Not with compex propertys, according to the rules of magic squares.

But ...

I think is very special, because it contains 3 squares in one!

64 x 64
Contains the numbers 1 - 4096, each ones
The sum of de rows, culumn and all diagonals is 131104

In de center there is another square
16 x 16
Contains the numbers 1 -256
The sum of de rows, culumn and all diagonals is 2056

And in de center of this 16 x 16 square is even a smaller one
4 x 4
Contains the numbers 1 -16
The sum of de rows, culumn and all diagonals is 34

Just look at it.

Do you like playing with numbers?

Fill the square - can you solve it?

But first read the rules beneath!

Post the answer in the reaction area, like

0000

0000

0000

0000

The rules

- Use every number (1-16) only ones

- The sum of each random row of 4 number is the numer X

 

- The sum of each random block of 2x2 is the number X

- The sum the corners of each random square is the number X

Can you make this puzzle?

Fill the square - can you solve it?

But first read the rules beneath!

Post the answer in the reaction area, like

0000

0000

0000

0000

The rules

- Use every number (1-16) only ones

- The sum of each random row of 4 number is the numer X

 

- The sum of each random block of 2x2 is the number X



- The sum the corners of each random square is the number X

How to make a perfect magic square manually! Part 1

Create a flawless magic square An - step by step - explanation of making a perfect magic square without computer. Any size is possible, as long as there is an order of 4x4 in it. So even 4 billion by 4 billion is possible, but takes quite a while. :) Formula for the sets (only for constant 1 to the right and n/4 down) A1 = (n²+1)-n²/16 A2 = (n²+1)+n²/16 horizontal sets B1 = (n²+1)-n²/8 B2 = (n²+1)+n²/8 vertical sets C1 = (n²+1)-n²/4 C2 = (n²+1)+n²/4 mirroring left -right D1 = (n²+1)-n²/2 D2 = (n²+1)+n²/2 mirroring top - bottom Example of the sets 8x8 square 20x20 square 8192x8192 square n = 8 n = 20 n = 8192 A1 = 61 A2 = 69 A1 = 376 A2 = 426 A1 = 62914561 A2 = 71303169 B1 = 57 B2 = 73 B1 = 351 B2 = 451 B1 = 58720257 B2 = 75497473 C1 = 49 C2 = 81 C1 = 301 C2 = 501 C1 = 50331649 C2 = 83886081 D1 = 33 D2 = 97 D1 = 201 D2 = 601 D1 = 33554433 D2 = 100663297 Pattern of the constant (repeating through the whole square) To the right + - - + = +1 -1 -1 +1 - + + - = -1 +1 +1 -1 Down + - = +n/4 -n/4 - + = -n/4 +n/4 - + = -n/4 +n/4 + - = +n/4 -n/4 Look at the very nice website https://www.magischvierkant.com/two-d... to see how magic this systeem of creating magic squares is (in English or Dutch) or look at Part 2 the demonstration of the extra magic aspects: https://youtu.be/6ApB7RolNZo