Breaking Down the Algorithm behind the 7x7 Magic Square

A magic square is a mathematical puzzle that involves arranging numbers in a square grid such that the sum of the numbers in each row, column, and diagonal is the same. Typically, magic squares are constructed using an odd number of rows and columns, with the most common being a 3x3 or a 5x5 grid. In the case of a magic square with 7 rows and 7 columns, the grid would contain a total of 49 cells. The numbers are usually arranged in ascending order from 1 to 49, starting from the top left corner and moving across each row. **The main idea here is constructing a magic square with 7 rows and 7 columns.** To create a magic square with 7 rows and 7 columns, certain rules and patterns can be followed.

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

This is a 3x3 used in Feng Shui which is represented as well 4 Wealth 9 Fame 2 Relationship 3 Family 5 Health 7 Children 8 Wiseness 1 Career 6 Help Friends. Then, because the numbering has now reached the top row, it has to be continued on the bottom row of the next column, which is why 122 is in the third column of the bottom row.

** To create a magic square with 7 rows and 7 columns, certain rules and patterns can be followed. One common pattern is known as the Siamese method, which involves starting with the number 1 in the middle cell of the top row. The next number is then placed diagonally above and to the right of the previous number.

Humongous Magic Square

Here is one of the biggest magic squares around. It is 15-by-15 squares in all. It was originally published by a German mathematician in 1604. (I got it from Mathematics From the Birth of Numbers. This is not only a nifty magic square, but the explanation that follows it below gives you a general method for creating odd-sided magic squares.

Did you find the pattern? Sort of? That's okay, it isn't completely clear until you're given the secret. So how does it work?

You begin by putting a 1 in the square that is just to the right of the center square (which is here the 8th row and 9th column). Then you enter increasing number, moving diagonally upward to the right. In this particular square you go from 1 to 7. Any time you reach the right side of the magic square is continued on the lefthand side of the magic square, one row up. So, in this case, since the 7 hits the last column in the second row, we put the 8 on row one starting in the far left column.

When you come to the top, or first, row, then you continue in on the bottom row of the next column. In this case, 8 happens to be in the top row in the first column, so we have put 9 in the bottom, or fifteenth, row of the next column (which is the second column in this case). Then you continue increasing your numbers diagonally up toward the right like before.

When you come to a square that already has a number in it, then you skip over that number and restart on the same row but two columns over. This happens when 15 runs into 1 in this magic square. Look and see where 16 in comparison to 15 in the magic square.

One special case in this magic square happens when 120 hits the upper right hand corner. Normally it would go in the bottom square of the far left column (the bottom left corner). But it is blocked by 106. So the two-step change gets made by putting 121 in the top square of the next column. Then, because the numbering has now reached the top row, it has to be continued on the bottom row of the next column, which is why 122 is in the third column of the bottom row.

You continue in this way until you get to the last space, and enter 225 just to the left of 113, which is in the center of the whole magic square.

Oh, by the way, did you figure out what every row, column, and diagonal adds up to? You can add one or two of them up if you wish, or you can do the following: Figure out the total number of squares (15 squared, actually, which = 15 X 15 = 225). Then multiply the total number of squares (225) by the total number of squares plus one (226) and divide the answer by 2. That equals (225 X 226) / 2 = 26,425. That's what the total of all of the squares is. Since there are 15 squares in each of the columns or rows and diagonals, you divide 26,425 by 15 and that equals 1,695, which is exactly what each and every row, column, and diagonal adds up to.

Now that's magic!

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When you come to a square that already has a number in it, then you skip over that number and restart on the same row but two columns over. This happens when 15 runs into 1 in this magic square. Look and see where 16 in comparison to 15 in the magic square.

If this would take the number outside of the grid, it is wrapped around to the opposite side. Following this pattern, the numbers are placed in the grid until all 49 cells are filled. At this point, the magic square should be complete, with each row, column, and diagonal adding up to the same constant value. Creating a magic square with 7 rows and 7 columns can be a challenging task, requiring careful arrangement and attention to detail. However, with the Siamese method and other techniques, it is possible to construct a satisfying puzzle that exhibits the properties of a magic square..

Reviews for "The Use of the 7x7 Magic Square in Number Theory"

- John - 1 star - This "Magic square with 7 rows and 7 columns" is anything but magical. The concept of a magic square is to have the sum of each row, column, and diagonal equal the same number, but this one fails to meet that criteria. The numbers seem randomly placed with no logic or pattern, making it impossible to solve. As a lover of puzzles and brain teasers, I found this to be a frustrating and disappointing experience.

- Sarah - 2 stars - I was excited to try the "Magic square with 7 rows and 7 columns" but was let down by its lack of clarity. The instructions were unclear and provided no guidance on how to solve or interact with the square. The numbers were haphazardly arranged, making it difficult to discern any patterns or logic. Overall, I found this puzzle to be confusing and unrewarding.

- Michael - 1 star - I found the "Magic square with 7 rows and 7 columns" to be completely uninteresting. The numbers were simply placed in a grid without any thought or creativity. As someone who enjoys puzzles, I was hoping for a challenge or at least an engaging experience, but this fell flat. I would not recommend wasting your time on this uninspiring magic square.

The Magic Numbers and Paths in the 7x7 Magic Square