How to create ramanujan magic square

How do you do Ramanujan magic square?

This is a super magic square because not only do the rows, columns, and diagonals add up to the same number, but the four corners, the four middle squares (17, 9, 24, 89), the first and last rows two middle numbers (12, 18, 86, 23), and the first and last columns two middle numbers (88, 10, 25, 16) all add up to the

How do you make a magic square?

How do you make a magic square in Java?

Creating a Magic Square in java
  1. Ask the user for an odd number.
  2. Create an n by n array.
  3. Follow these steps to create a magic square. a. Place a 1 in the middle of the first row. b. Subtract 1 from the row and add 1 to the column. i. If possible place the next number at that position. ii. If not possible, follow these steps.
  4. Print the array.

What is the easiest way to solve a magic square?

Magic Square Solution
  1. List the numbers in order from least to greatest on a sheet of paper.
  2. Add all nine of the numbers on your list up to get the total.
  3. Divide the total from Step 2 by 3.
  4. Go back to your list of numbers and the number in the very middle of that list will be placed in the center of the magic square.

How many solutions are there to a 3×3 magic square?

There are 8 possible magic squares for 3 X 3 matrix.

How does a magic square work?

A magic square is an n x n square with a whole number written inside each cell, so that the sum of the numbers in every row, in every column and in each of the main diagonals is equal. This number is called the magic number. The main diagonals are those that stretch from corner to corner.

Why does a magic square work?

Magic Squares are square grids with a special arrangement of numbers in them. These numbers are special because every row, column and diagonal adds up to the same number. Also, the two numbers that are opposite each other across the centre number will add up to the same number.

What is the magic number of a magic square?

A magic square is a grid containing the numbers 1, 2, 3, and so on, where each row, column and diagonal add up to the same number. An example is shown below, you will see that each row, column and diagonal add up to 34. This number 34 is the “magic number” of the magic square.

What is a magic square used for?

It takes a great deal of skill to be able to arrange numbers in a square to make all the rows, columns, and diagonals have the same sum. The use of magic squares dates back as far as the ancient Chinese and they are still used today as challenging math puzzles.

Why is 28 the perfect number?

A number is perfect if all of its factors, including 1 but excluding itself, perfectly add up to the number you began with. 6, for example, is perfect, because its factors — 3, 2, and 1 — all sum up to 6. 28 is perfect too: 14, 7, 4, 2, and 1 add up to 28.

Why number 9 is magic?

Answer. (1) When you multiply nine by any number and add up the digits of the answer, you get 9. (2) The difference between a positive integer and the sum of its digits (or digital root) is a multiple of nine. The digital root of 27 is 2+7 = 9, which means it is evenly divisible by nine.

Is Sudoku a magic square?

No. Sudoku is a particular type of number puzzle/game. A magic square is a particular case of n**2 numbers in a n x n grid. A correctly solved sudoku puzzle has some elements of a magic square, but not all, so it also is not a magic square.

What is the math behind sudoku?

To solve a Sudoku puzzle, one needs to use a combination of logic and trial-and-error. More math is involved behind the scenes: combinatorics used in counting valid Sudoku grids, group theory used to describe ideas of when two grids are equivalent, and computational complexity with regards to solving Sudokus.

Can a sudoku be unsolvable?

Nope, it’s impossible. By definition, a Sudoku puzzle has one and only one solution. If you personally can‘t solve a particular puzzle, that doesn’t make it unsolvable.

What is a magic square Sudoku?

A magic square is a square grid filled with numbers, in such a way that each row, each column, and the two diagonals add up to the same number. It has three rows and three columns, and if you add up the numbers in any row, column or diagonal, you always get 15.

How do you arrange a 1 9 in a square?

You can assemble the numbers 1 to 9 in a square, so that the sum of the rows, the columns, and the diagonals is 15. If you take the numbers 1 to 9, you have the standard square. A magic square remains magic, if you change each numbers by a constant c.

How do you solve a 4 by 4 magic square?

How do you solve a Sudoku Magic Square?

Place numbers in the grid such that every row, column and 3×3 box contain the numbers 1 to 9. Shaded 3×3 squares are magic squares. The sum of the numbers in all rows, columns and two diagonals should be equal in a magic square.

Who invented magic square?

In the 18th century, Leonhard Euler, the greatest mathematician of his day, was devising ways to create magic squares.

How many squares do you see 3×3?

A 3×3 grid

There are 9 + 4 + 1 = 14 total squares.

Can you repeat numbers in a magic square?

The numbers in every row add up to the same number. As you can see all the rows add up to 15. Notice that each number from 1 to 9 is used once. If you could repeat numbers, many magic squares would become trivially easy, like a grid made entirely of 1s that added up to 3!

What 4 numbers add up to 34?

Then 9+9+8+8=34. Yes finally!

How do you solve positive and negative magic squares?