# Split N^2 numbers into N groups of equal sum

Given an even number N. The task is to consider numbers from 1 to N2, split them into N groups of the equal sum.

Examples:

```Input: N = 2
Output: {1, 4}, {2, 3}
Two groups of equal sum are 1, 4 and 2,3

Input: N = 4
Output:
{ 1, 16} { 2, 15}
{ 3, 14} { 4, 13}
{ 5, 12} { 6, 11}
{ 7, 10} { 8, 9}
```

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

Approach: Formula for sum of first N2 numbers: Sum = (N2 * (N2 + 1))/ 2.

Therefore, the sum of each group would be = (N2 + 1)* N2 / 2

Let us consider pairs of the following type (1, N2), (2, N2-1) and so on.

Since N2 is an even number, each group can be made using exactly N/2 such pairs.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to print N groups of equal sum ` `void` `printGroups(``int` `n) ` `{ ` `    ``int` `x = 1; ` `    ``int` `y = n * n; ` ` `  `    ``// No. of Groups ` `    ``for` `(``int` `i = 1; i <= n; i++) { ` ` `  `        ``// n/2 pairs ` `        ``for` `(``int` `j = 1; j <= n / 2; j++) { ` `            ``cout << ``"{ "` `<< x << ``", "` `<< y << ``"} "``; ` `            ``x++; ` `            ``y--; ` `        ``} ` ` `  `        ``cout << endl; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 4; ` `    ``printGroups(n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the above approach ` ` `  `import` `java.io.*; ` ` `  `class` `GFG { ` `     `  ` `  ` `  `// Function to print N groups of equal sum ` `static` `void` `printGroups(``int` `n) ` `{ ` `    ``int` `x = ``1``; ` `    ``int` `y = n * n; ` ` `  `    ``// No. of Groups ` `    ``for` `(``int` `i = ``1``; i <= n; i++) { ` ` `  `        ``// n/2 pairs ` `        ``for` `(``int` `j = ``1``; j <= n / ``2``; j++) { ` `            ``System.out.print(``"{ "` `+ x + ``", "` `+ y + ``"} "``); ` `            ``x++; ` `            ``y--; ` `        ``} ` ` `  `        ``System.out.println(); ` `    ``} ` `} ` ` `  `// Driver code ` ` `  `    ``public` `static` `void` `main (String[] args) { ` `            ``int` `n = ``4``; ` `    ``printGroups(n); ` `    ``} ` `} ` `// This code is contributed by shs `

## Python3

 `# Python implementation of the above approach ` ` `  `# Function to print N groups of equal sum ` `def` `printGroups(n) : ` `     `  `    ``x ``=` `1` `    ``y ``=` `n ``*` `n ` `     `  `    ``# No. of Groups ` `    ``for` `i ``in` `range``(``1``, n ``+` `1``) : ` `         `  `        ``# n/2 pairs ` `        ``for` `j ``in` `range``(``1``, n ``/``/` `2` `+` `1``) : ` `             `  `            ``print``(``"{"``,x,``","``,y,``"}"``,end ``=` `" "``) ` `             `  `            ``x ``+``=` `1` `            ``y ``-``=` `1` `         `  `        ``print``() ` `         `  `        `  `# Driver code ` `if` `__name__ ``=``=` `"__main__"` `: ` `     `  `    ``n ``=` `4` `     `  `    ``# Function call ` `    ``printGroups(n) ` ` `  `# This code is contributed by Ryuga `

## C#

 `// Java implementation of the  ` `// above approach ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `     `  `// Function to print N groups  ` `// of equal sum ` `static` `void` `printGroups(``int` `n) ` `{ ` `    ``int` `x = 1; ` `    ``int` `y = n * n; ` ` `  `    ``// No. of Groups ` `    ``for` `(``int` `i = 1; i <= n; i++)  ` `    ``{ ` ` `  `        ``// n/2 pairs ` `        ``for` `(``int` `j = 1; j <= n / 2; j++) ` `        ``{ ` `            ``Console.Write(``"{ "` `+ x + ``", "` `+ y + ``"} "``); ` `            ``x++; ` `            ``y--; ` `        ``} ` ` `  `        ``Console.WriteLine(); ` `    ``} ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main () ` `{ ` `    ``int` `n = 4; ` `    ``printGroups(n); ` `} ` `} ` ` `  `// This code is contributed by shs `

## PHP

 ` `

Output:

```{ 1, 16} { 2, 15}
{ 3, 14} { 4, 13}
{ 5, 12} { 6, 11}
{ 7, 10} { 8, 9}
``` My Personal Notes arrow_drop_up Check out this Author's contributed articles.

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