Magic square generator


  • C Programming – Magic Square
  • CPP Program to generate magic squares
  • 3x3 Magic Square
  • Magic Square | ODD Order
  • Magic Squares: A Detailed Strategy Guide​
  • C Programming – Magic Square

    You can watch the video below for a more in-depth explanation. From there, I just played with the numbers a bit using Google Sheets to avoid tedious manual calculations and pretty quickly found a solution. For one, I could see that if I split the numbers into groups , , , I had balanced the grid by ensuring that no number of the same group shared a row or column.

    But with a 4-by-4 grid, there is no middle… so how would that work? Ignoring that temporarily, my initial idea was to look at each number group as a different color, and set up the 4-by-4 grid so that no two boxes of the same color shared a row or column, just to simplify the process I used for the 3-by I figured that after finding that grid, I could swap the numbers in each group among the boxes with their assigned color, and things would just fall into place.

    Wrong, again. Two hours into tinkering around with the numbers, my frustration got the best of me. I set up the 4-by-4 grid again, ignoring every rule I had set for myself before.

    To my surprise, the diagonals added up perfectly. It took about 20 seconds for me to finish the puzzle from there. First, I swapped the lowest and highest numbers at the top and bottom middle two squares, not in the diagonals and flipped their order. Then I did the same for the left and right. Could solving a magic square really be that simple?

    Solving a Doubly-Even Square It turns out, no. Essentially, if you follow the same pattern for an 8-by-8 grid, you keep the 4-by-4 box in the middle and the 2-by-2 boxes in each of the corners the same, and swap the other numbers accordingly.

    If you examine this grid, you can see that the swapping of numbers becomes more involved as the square gets bigger, but can still be solved in an ordered fashion. Solving an Odd-Numbered Square When it came to odd-numbered grids, after a while of trying to find a pattern, I gave in and did a quick Google search. Turns out, there is a pretty specific and simple pattern for finding an odd-numbered magic square. Start with 1 in the top middle box, then place the next number up one box and to the right one box.

    If its place goes off the right edge of the grid, keep the number in the same row, but move it to the leftmost column of the grid. If its place is already taken by an existing number or it goes off the right top corner , place the new number directly below the last number you placed.

    After careful examination, it became apparent that you could simply swap a few of the numbers to achieve the perfect balance. A more clear pattern emerges once you start getting into the bigger squares, but the same basic switch between upper and lower quadrants still occurs.

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    CPP Program to generate magic squares

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    3x3 Magic Square

    Magic Square | ODD Order

    I set up the 4-by-4 grid again, ignoring every rule I had set for myself before. To my surprise, the diagonals added up perfectly. It took about 20 seconds for me to finish the puzzle from there. First, I swapped the lowest and highest numbers at the top and bottom middle two squares, not in the diagonals and flipped their order. Then I did the same for the left and right.

    Could solving a magic square really be that simple? Solving a Doubly-Even Square It turns out, no. Essentially, if you follow the same pattern for an 8-by-8 grid, you keep the 4-by-4 box in the middle and the 2-by-2 boxes in each of the corners the same, and swap the other numbers accordingly.

    Our online coding, design, chess and math courses are designed to suit kids' learning pace. We not only teach kids the basics of coding, maths and design, but also make them proficient in logical thinking that enable kids to create wonderful games, animations, and apps. About CodingHero At CodingHero, the kids start learning through our online classes for coding, design, chess and maths.

    Magic Squares: A Detailed Strategy Guide​

    Our online courses introduce the kids from 5 years of age to the whole new exciting world of coding by learning web development, game development, chess strategies and moves, maths concepts, and mobile app development and that too from the comfort of your home.

    After mentioning grid size, you can generate magic square for a specific magic sum value or for a minimal magic sum value. If you only mention the grid size, it creates the magic square with minimal sum value by default. Unlike others, this tool also uses negative and decimal values to generate magic square which gives you the flexibility to generate magic square for any value of the magic sum.

    Here, you can generate magic square for any magic sum value in between 0 to It also tells you how many 4 cells combinations are there which add up to the sum value. The magic squares of 3, 4 and 5 grid size are the main focus here. For these grid sizes, you can generate magic square by defining a pattern rather than using magic sum value as input.


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