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The Witch Queen is an upcoming expansion for the popular video game Destiny 2. It is set to release in early 2022 and is highly anticipated by fans of the franchise. The expansion will introduce new story content, missions, and weapons for players to experience. **The main highlight of this expansion is the introduction of a new villain, Savathûn, the Witch Queen herself. She is a powerful Hive god and has long been a significant figure in the game's lore.** Players will have to face off against her and her hive armies as they try to protect the Last City and defeat this ancient threat.

For 3x3, 4x4, 5x5 and 7x7 squares, the smallest possible maximum number is always possible with the smallest P. But it is not the case for 6x6 squares! Here is an example with the smallest possible maximum number for 6x6 squares, but needing a bigger P:

Since 14 4 3 2 and n 3, we might guess that if we change the first three columns, except for the diagonal elements, and the last two rows, we might get a 14 14 magic square. A is a grid of numbers arranged so that the sum of each row, each column and its diagonals are all equal to the same value, called the magic sum or magic constant.

** Players will have to face off against her and her hive armies as they try to protect the Last City and defeat this ancient threat. In addition to the new story content, the expansion will also bring new gameplay features, such as new subclasses and abilities for players to master. With its promise of new challenges and a compelling story, The Witch Queen expansion is sure to be a hit among Destiny 2 players.

Magic Square

A is a grid of numbers arranged so that the sum of each row, each column and its diagonals are all equal to the same value, called the magic sum (or magic constant).

are popular for their simplicity and mathematical properties.

How to create a magic square?

A arranges numbers so that their placement follows construction rules that ensure that the sums of rows, columns, and diagonals equal the magic sum.

Construction methods vary depending on the order of the square (number of rows/columns).

How to create a magic square of odd order?

The creation of of size (3,5,7 etc.) is possible by several methods, the simplest is the so-called Loubère method (staircase method):

Place 1 in the center of the first line, then the following numbers in the box located diagonally at the top left. If the box is outside the square, imagine that the square wraps around itself and continue on the other end (as if the left column were to the right of the right column, and the bottom line, at the above the top line). If the target square is occupied, then continue directly below the last filled square.

Example: Staircase method generating a of order 3:

Example: Staircase method generating a of order 5 :

How to create a magic square of even order?

Creating of even order (4,6,8, etc.) is more complicated and the methods are not universal.

Symmetry method for squares of size 4:

— Place the numbers naturally from 1 at the top left to 16 at the bottom right.

— Replace the numbers on the sides (2, 3, 5 and 9) by their central symmetry (relative to the center of the square).

Other methods generally rely on creating odd subsquares.

How to solve a magic square?

The magic way to solve is to set the equations that govern each row and column, with unknowns. The constraints being that the unknowns are all different positive integers (distinct including numbers already placed).

Example: The of magic value $ X $

The equations obtained sometimes have several solutions.

What are the minimal possible sums (magic values)?

The constant values $ M $ of the sums of the have a minimum value (for non-zero integer positive values).

For a size 3x3, the minimum constant is 15, for 4x4 it is 34, for 5x5 it is 65, 6x6 it is 111, then 175, 260, …

Any lower sum will force the use of either negative numbers or fractions (not whole numbers) to solve the .

What are the maximal possible sums (magic values)?

The values can be as large as you want, so the maximum magic sum/value is infinity.

What is a panmagic square?

A panmagic square, also called a pandiagonal square, is a special type of . Unlike traditional , where only rows, columns, and major diagonals have equal sums, a panmagic square has an additional property: the sums of the numbers along all its diagonals (including minor diagonals) are equal. also equal to the magic sum.

Is there a Magic Square in 3D (Magic Cube)?

Yes, there are magic cubes, their magic value is $$ M = n(n^3+1)/2 $$ (which may or may not have magic diagonals)

What is the Franklin Square?

Franklin's square, published in 1769 by Benjamin Franklin, is a semi-panmagic square with a magic constant of 260.

Example:

What is the Lo-Shu Magic Square?

This is a 3x3 used in Feng Shui which is represented as well

What is the KaldorMagic Square?

Kaldor's is a square used in economics, which has nothing to do with digits or numbers of mathematics but rather with concepts from economic policy.

Overall, fans can expect an exciting and thrilling experience as they dive into Destiny 2: The Witch Queen and face off against Savathûn, the powerful Witch Queen of the Hive..

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