Skip to content
Related Articles
Smallest number whose sum of digits is square of N
• Last Updated : 24 Mar, 2021

Given an integer N, the task is to find the smallest number whose sum of digits is N2.
Examples:

Input: N = 4
Output: 79
24 = 16
sum of digits of 79 = 76
Input: N = 6
Output: 9999
210 = 1024 which has 4 digits

Approach: The idea is to find the general term for the smallest number whose sum of digits is square of N. That is

```// First Few terms
First Term = 1 // N = 1
Second Term = 4 // N = 2
Third Term = 9 // N = 3
Fourth Term = 79 // N = 4
.
.
Nth Term:```

```*** QuickLaTeX cannot compile formula:

*** Error message:
Error: Nothing to show, formula is empty
```

` <sup>(n^2 \% 9 + 1) * 10 ^ {\lfloor n^2/9 \rfloor} - 1 </sup>`

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach` `#include ``using` `namespace` `std;` `// Function to return smallest``// number whose sum of digits is n^2``int` `smallestNum(``int` `n)``{``  ``cout<<``pow``(10, n * n / 9)<

## Java

 `// Java implementation of the above approach``import` `java.util.*;` `class` `GFG{` `// Function to return smallest``// number whose sum of digits is n^2``static` `int` `smallestNum(``int` `n)``{``    ``return` `(``int``)((n * n % ``9` `+ ``1``) *``         ``Math.pow(``10``, n * n / ``9``) - ``1``);``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `n = ``4``;``    ` `    ``System.out.print(smallestNum(n));``}``}` `// This code is contributed by Rajput-Ji`

## Python 3

 `# Python implementation of the above approach` `# Function to return smallest``# number whose sum of digits is n^2``def` `smallestNum(n):` `    ``return` `((n ``*` `n ``%` `9` `+` `1``)  ``*``          ``pow``(``10``, ``int``(n ``*` `n ``/` `9``)) ``-` `1``)` `# Driver Code` `# Given N``N ``=` `4` `print``(smallestNum(N))` `# This code is contributed by Vishal Maurya.`

## C#

 `// C# implementation of the above approach``using` `System;` `class` `GFG{` `// Function to return smallest``// number whose sum of digits is n^2``static` `int` `smallestNum(``int` `n)``{``    ``return` `(``int``)((n * n % 9 + 1) *``         ``Math.Pow(10, n * n / 9) - 1);``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``int` `n = 4;``    ` `    ``Console.Write(smallestNum(n));``}``}` `// This code is contributed by Rajput-Ji`

## Javascript

 ``

Output:

`79`

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.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with industry experts, please refer DSA Live Classes

My Personal Notes arrow_drop_up