# Find a number x such that sum of x and its digits is equal to given n.

Given a positive number n. We need to find a number x such that sum of digits of x to itself is equal to n.

If no such x is possible print -1.**Examples:**

Input : n = 21 Output : x = 15 Explanation : x + its digit sum = 15 + 1 + 5 = 21 Input : n = 5 Output : -1

We iterate from 1 to n and for each intermediate number, x find its digit sum and then add that to x, if that is equal to n then x will be our required answer.

// iterate from 1 to n. For every no. // check if its digit sum with it is // equal to n. for (int i = 0; i <= n; i++) if (i + digSum(i) == n) return i; return -1;

## C++

`// CPP program to find x such that x +` `// digSum(x) is equal to n.` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// utility function for digit sum` `int` `digSum(` `int` `n)` `{` ` ` `int` `sum = 0, rem = 0;` ` ` `while` `(n) {` ` ` `rem = n % 10;` ` ` `sum += rem;` ` ` `n /= 10;` ` ` `}` ` ` `return` `sum;` `}` `// function for finding x` `int` `findX(` `int` `n)` `{` ` ` `// iterate from 1 to n. For every no.` ` ` `// check if its digit sum with it is` ` ` `// equal to n.` ` ` `for` `(` `int` `i = 0; i <= n; i++)` ` ` `if` `(i + digSum(i) == n)` ` ` `return` `i;` ` ` ` ` `// if no such i found return -1` ` ` `return` `-1;` `}` `// driver function` `int` `main()` `{` ` ` `int` `n = 43;` ` ` `cout << ` `"x = "` `<< findX(n);` ` ` `return` `0;` `}` |

## Java

`// Java program to find x such that x +` `// digSum(x) is equal to n.` `class` `GFG` `{` ` ` ` ` `// utility function for digit sum` ` ` `static` `int` `digSum(` `int` `n)` ` ` `{` ` ` `int` `sum = ` `0` `, rem = ` `0` `;` ` ` ` ` `while` `(n>` `0` `) {` ` ` `rem = n % ` `10` `;` ` ` `sum += rem;` ` ` `n /= ` `10` `;` ` ` `}` ` ` ` ` `return` `sum;` ` ` `}` ` ` ` ` `// function for finding x` ` ` `static` `int` `findX(` `int` `n)` ` ` `{` ` ` ` ` `// iterate from 1 to n. For every no.` ` ` `// check if its digit sum with it is` ` ` `// equal to n.` ` ` `for` `(` `int` `i = ` `0` `; i <= n; i++)` ` ` `if` `(i + digSum(i) == n)` ` ` `return` `i;` ` ` ` ` `// if no such i found return -1` ` ` `return` `-` `1` `;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `int` `n = ` `43` `;` ` ` ` ` `System.out.println(` `"x = "` `+findX(n));` ` ` `}` `}` `// This code is contributed by Anant Agarwal.` |

## Python3

`# Python3 program to find` `# x such that dx + igSum(x)` `# is equal to n.` `# utility function` `# for digit sum` `def` `digSum(n):` ` ` `sum` `=` `0` `;` ` ` `rem ` `=` `0` `;` ` ` `while` `(n):` ` ` `rem ` `=` `n ` `%` `10` `;` ` ` `sum` `=` `sum` `+` `rem;` ` ` `n ` `=` `int` `(n ` `/` `10` `);` ` ` `return` `sum` `;` `# function for finding x` `def` `findX(n):` ` ` ` ` `# iterate from 1 to n.` ` ` `# For every no.` ` ` `# check if its digit` ` ` `# sum with it is# equal to n.` ` ` `for` `i ` `in` `range` `(n ` `+` `1` `):` ` ` `if` `(i ` `+` `digSum(i) ` `=` `=` `n):` ` ` `return` `i;` ` ` ` ` `# if no such i` ` ` `# found return -1` ` ` `return` `-` `1` `;` `# Driver Code` `n ` `=` `43` `;` `print` `(` `"x = "` `, findX(n));` `# This code is contributed by mits` |

## C#

`// C# program to find x such that` `// x + digSum(x) is equal to n.` `using` `System;` `class` `GFG {` ` ` ` ` `// utility function for digit sum` ` ` `static` `int` `digSum(` `int` `n)` ` ` `{` ` ` `int` `sum = 0, rem = 0;` ` ` ` ` `while` `(n > 0)` ` ` `{` ` ` `rem = n % 10;` ` ` `sum += rem;` ` ` `n /= 10;` ` ` `}` ` ` ` ` `return` `sum;` ` ` `}` ` ` ` ` `// function for finding x` ` ` `static` `int` `findX(` `int` `n)` ` ` `{` ` ` ` ` `// iterate from 1 to n. For every no.` ` ` `// check if its digit sum with it is` ` ` `// equal to n.` ` ` `for` `(` `int` `i = 0; i <= n; i++)` ` ` `if` `(i + digSum(i) == n)` ` ` `return` `i;` ` ` ` ` `// if no such i found return -1` ` ` `return` `-1;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `n = 43;` ` ` ` ` `Console.Write(` `"x = "` `+ findX(n));` ` ` `}` `}` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP program to find x such that` `// dx + igSum(x) is equal to n.` `// utility function` `// for digit sum` `function` `digSum(` `$n` `)` `{` ` ` `$sum` `= 0; ` `$rem` `= 0;` ` ` `while` `(` `$n` `)` ` ` `{` ` ` `$rem` `= ` `$n` `% 10;` ` ` `$sum` `+= ` `$rem` `;` ` ` `$n` `/= 10;` ` ` `}` ` ` `return` `$sum` `;` `}` `// function for finding x` `function` `findX(` `$n` `)` `{` ` ` ` ` `// iterate from 1 to n.` ` ` `// For every no.` ` ` `// check if its digit` ` ` `// sum with it is` ` ` `// equal to n.` ` ` `for` `(` `$i` `= 0; ` `$i` `<= ` `$n` `; ` `$i` `++)` ` ` `if` `(` `$i` `+ digSum(` `$i` `) == ` `$n` `)` ` ` `return` `$i` `;` ` ` ` ` `// if no such i` ` ` `// found return -1` ` ` `return` `-1;` `}` ` ` `// Driver Code` ` ` `$n` `= 43;` ` ` `echo` `"x = "` `, findX(` `$n` `);` `// This code is contributed by vt_m.` `?>` |

## Javascript

`<script>` `// Javascript program to find x such that x +` `// digSum(x) is equal to n.` ` ` ` ` `// utility function for digit sum` ` ` `function` `digSum(n)` ` ` `{` ` ` `let sum = 0, rem = 0;` ` ` ` ` `while` `(n>0) {` ` ` `rem = n % 10;` ` ` `sum += rem;` ` ` `n = Math.floor(n / 10);` ` ` `}` ` ` ` ` `return` `sum;` ` ` `}` ` ` ` ` `// function for finding x` ` ` `function` `findX(n)` ` ` `{` ` ` ` ` `// iterate from 1 to n. For every no.` ` ` `// check if its digit sum with it is` ` ` `// equal to n.` ` ` `for` `(let i = 0; i <= n; i++)` ` ` `if` `(i + digSum(i) == n)` ` ` `return` `i;` ` ` ` ` `// if no such i found return -1` ` ` `return` `-1;` ` ` `}` `// driver program` ` ` `let n = 43;` ` ` ` ` `document.write(` `"x = "` `+findX(n));` ` ` `</script>` |

**Output:**

x = 35

This article is contributed by **Shivam Pradhan (anuj_charm)**. 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.

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