# Place N^2 numbers in matrix such that every row has an equal sum

Given a number N, place numbers from the range [1, N^{2}] in an NxN matrix such that sum in every row is equal.

**Examples:**

Input:N = 3Output:1 5 9 2 6 7 3 4 8 Sum in 1st row: 15 Sum in 2nd row: 15 Sum in 2nd row: 15Input:N = 5Output:1 7 13 19 25 2 8 14 20 21 3 9 15 16 22 4 10 11 17 23 5 6 12 18 24

A **Greedy Approach **has been used to fill the matrix, where the insertion of elements in the matrix is done row-wise. The required matrix can be obtained using below steps:

- Fill the matrix initially with numbers in the range [1, N
^{2}] using matrix traversal. - Traverse the matrix and change every position in a new matrix considering it as answer matrix by
**answer[i][j] = mat[j][(i+j)%n].**

Below is the implementation of the above approach:

`// Java program to distribute n^2 numbers to n people ` `public` `class` `Numbers { ` ` ` `public` `static` `int` `[][] solve(` `int` `[][] arr, ` `int` `n) ` ` ` `{ ` ` ` `// 2D array for storing the final result ` ` ` `int` `[][] ans = ` `new` `int` `[n][n]; ` ` ` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++) { ` ` ` `for` `(` `int` `j = ` `0` `; j < n; j++) { ` ` ` `// using modulo to go to the firs ` ` ` `// column after the last column ` ` ` `ans[i][j] = arr[j][(i + j) % n]; ` ` ` `} ` ` ` `} ` ` ` `return` `ans; ` ` ` `} ` ` ` `public` `static` `void` `show(` `int` `[][] arr, ` `int` `n) ` ` ` `{ ` ` ` `int` `[][] res = solve(arr, n); ` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++) { ` ` ` ` ` `for` `(` `int` `j = ` `0` `; j < n; j++) { ` ` ` `System.out.print(res[i][j] + ` `" "` `); ` ` ` `} ` ` ` `System.out.println(); ` ` ` `} ` ` ` `} ` ` ` `// making a 2D array containing numbers ` ` ` `public` `static` `int` `[][] makeArray(` `int` `n) ` ` ` `{ ` ` ` `int` `[][] arr = ` `new` `int` `[n][n]; ` ` ` `int` `c = ` `1` `; ` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++) { ` ` ` `for` `(` `int` `j = ` `0` `; j < n; j++) ` ` ` `arr[i][j] = c++; ` ` ` `} ` ` ` `return` `arr; ` ` ` `} ` ` ` ` ` `// Driver Code ` ` ` `public` `static` `void` `main(String[] args) ` ` ` `{ ` ` ` `int` `n = ` `5` `; ` ` ` `int` `[][] arr = makeArray(n); ` ` ` `show(arr, n); ` ` ` `} ` `} ` |

*chevron_right*

*filter_none*

**Output:**

1 7 13 19 25 2 8 14 20 21 3 9 15 16 22 4 10 11 17 23 5 6 12 18 24

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