Overview

A magic square is a square array of numbers where the sum of each row, column, and diagonal is the same. Your task is to write a program that determines if a given 2D array is a magic square.

For example, this is a magic square (sum = 15):

8 1 6
3 5 7
4 9 2

This is not a magic square:

1 2 3
4 5 6
7 8 9

Assignment Requirements

Write the following methods to help determine if a square array is a magic square:

1. Row Sum

/**
 * Returns the sum of a specified row in the array
 * @param square the 2D array to process
 * @param row the row index to sum
 * @return the sum of all elements in the specified row
 */
public static int rowSum(int[][] square, int row)

2. Column Sum

/**
 * Returns the sum of a specified column in the array
 * @param square the 2D array to process
 * @param col the column index to sum
 * @return the sum of all elements in the specified column
 */
public static int colSum(int[][] square, int col)

3. Diagonal Sums

/**
 * Returns the sum of the main diagonal (top-left to bottom-right)
 * @param square the 2D array to process
 * @return the sum of elements along the main diagonal
 */
public static int mainDiagSum(int[][] square)

/**
 * Returns the sum of the other diagonal (top-right to bottom-left)
 * @param square the 2D array to process
 * @return the sum of elements along the other diagonal
 */
public static int otherDiagSum(int[][] square)

4. Magic Square Check

/**
 * Determines if the given square array is a magic square.
 * A magic square must:
 * 1. Be square (same number of rows and columns)
 * 2. Have all row sums equal to each other
 * 3. Have all column sums equal to each other
 * 4. Have both diagonal sums equal to the row/column sums
 *
 * @param square the 2D array to check
 * @return true if the array is a magic square, false otherwise
 */
public static boolean isMagicSquare(int[][] square)

Testing

Test your methods with at least these cases:

  1. A valid 3x3 magic square: 
    int[][] valid = {
 {8, 1, 6},
 {3, 5, 7},
 {4, 9, 2}
};
  2. An invalid 3x3 square: 
    int[][] invalid = {
 {1, 2, 3},
 {4, 5, 6},
 {7, 8, 9}
};
  3. A non-square array: 
    int[][] notSquare = {
 {1, 2, 3},
 {4, 5, 6}
};

Implementation Tips

  1. Start by writing and testing each helper method individually
  2. For isMagicSquare, first check if the array is square
  3. Then check if any row sum equals any column sum
  4. Finally check if both diagonal sums equal the row/column sums
  5. Use a constant variable to store the “magic sum” once you find it
  6. Remember to handle edge cases (null arrays, empty arrays, non-square arrays)
  7. Your solution should work on any square array not just 3x3.

Bonus Challenge

Extend your program to:

  1. Verify that each number 1 through n² appears exactly once
  2. Find the magic constant based on array size (it should be n(n²+1)/2 where n is the size)
  3. Create a magic square of a given size $n$

Example Output

Your program should provide clear output, for example:

Testing magic square:
8 1 6
3 5 7
4 9 2

Row sums: 15, 15, 15
Column sums: 15, 15, 15
Diagonal sums: 15, 15

Result: This is a magic square!