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

Given a number N, place numbers from the range [1, N2] in an NxN matrix such that sum in every row is equal.

Examples:

```Input: N = 3
Output: 1 5 9
2 6 7
3 4 8
Sum in 1st row: 15
Sum in 2nd row: 15
Sum in 2nd row: 15

Input: N = 5
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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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, N2] 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); ` `    ``} ` `} `

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
```

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.