# Count three-digit numbers having difference X with its reverse

Given an integer **X**, the task is to count the total number of three-digit numbers having difference** X** with its reverse. If no such number exists, then print -1.

**Examples:**

Input:X = 792Output :10Explanation :

901 – 109 = 792

911 – 119 = 792

921 – 129 = 792

931 – 139 = 792

941 – 149 = 792

951 – 159 = 792

961 – 169 = 792

971 – 179 = 792

981 – 189 = 792

991 – 199 = 792

Input:X = 0Output:90

**Approach:** The given problem can be solved based on the following observations:

Let N = rpq

Therefore, N = 100r + 10q + p

Therefore, reverse of N = 100p + 10q + r

Therefore, the problem reduces to solving (100r + 10q + p) – (r + 10q + 100p) = X

-> 99(r – p) = X

-> r – p = X / 99

Therefore, if givenXis a multiple of 99, then solution exists.

Follow the steps below to solve the problem based on the above observations:

- Check if X is multiple of 99 or not. If not found to be true, print -1 as no solution exists.
- Otherwise, calculate
**X / 99**. Generate all pairs using digits [1, 9] and for each pair, check if their difference is equal to**X / 99**or not. - If found to be true for any pair, increase count by 10, as the middle digit can be permuted to place any value from the range [0, 9] for the obtained pair.
- Finally, print the value of the count obtained.

Below is the implementation of the above approach:

## C++

`// C++ Program to implement` `// the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to count three-digit` `// numbers having difference x` `// with its reverse` `int` `Count_Number(` `int` `x)` `{` ` ` `int` `ans = 0;` ` ` `// if x is not multiple of 99` ` ` `if` `(x % 99 != 0) {` ` ` `// No solution exists` ` ` `ans = -1;` ` ` `}` ` ` `else` `{` ` ` `int` `diff = x / 99;` ` ` `// Generate all possible pairs` ` ` `// of digits [1, 9]` ` ` `for` `(` `int` `i = 1; i < 10; i++) {` ` ` `for` `(` `int` `j = 1; j < 10; j++) {` ` ` `// If any pair is obtained` ` ` `// with difference x / 99` ` ` `if` `((i - j) == diff) {` ` ` `// Increase count` ` ` `ans += 10;` ` ` `}` ` ` `}` ` ` `}` ` ` `}` ` ` `// Return the count` ` ` `return` `ans;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `x = 792;` ` ` `cout << Count_Number(x) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java program to implement` `// the above approach` `import` `java.io.*;` `import` `java.util.Arrays;` `class` `GFG{` ` ` `// Function to count three-digit` `// numbers having difference x` `// with its reverse` `static` `int` `Count_Number(` `int` `x)` `{` ` ` `int` `ans = ` `0` `;` ` ` ` ` `// If x is not multiple of 99` ` ` `if` `(x % ` `99` `!= ` `0` `)` ` ` `{` ` ` ` ` `// No solution exists` ` ` `ans = -` `1` `;` ` ` `}` ` ` `else` ` ` `{` ` ` `int` `diff = x / ` `99` `;` ` ` ` ` `// Generate all possible pairs` ` ` `// of digits [1, 9]` ` ` `for` `(` `int` `i = ` `1` `; i < ` `10` `; i++)` ` ` `{` ` ` `for` `(` `int` `j = ` `1` `; j < ` `10` `; j++)` ` ` `{` ` ` ` ` `// If any pair is obtained` ` ` `// with difference x / 99` ` ` `if` `((i - j) == diff)` ` ` `{` ` ` ` ` `// Increase count` ` ` `ans += ` `10` `;` ` ` `}` ` ` `}` ` ` `}` ` ` `}` ` ` ` ` `// Return the count` ` ` `return` `ans;` `}` ` ` `// Driver Code` `public` `static` `void` `main (String[] args)` `{` ` ` `int` `x = ` `792` `;` ` ` ` ` `System.out.println(Count_Number(x));` `}` `}` `// This code is contributed by sanjoy_62` |

## Python3

`# Python3 program to implement` `# the above approach` `# Function to count three-digit` `# numbers having difference x` `# with its reverse` `def` `Count_Number(x):` ` ` ` ` `ans ` `=` `0` `;` ` ` `# If x is not multiple` ` ` `# of 99` ` ` `if` `(x ` `%` `99` `!` `=` `0` `):` ` ` `# No solution exists` ` ` `ans ` `=` `-` `1` `;` ` ` `else` `:` ` ` `diff ` `=` `x ` `/` `99` `;` ` ` `# Generate all possible pairs` ` ` `# of digits [1, 9]` ` ` `for` `i ` `in` `range` `(` `1` `, ` `10` `):` ` ` `for` `j ` `in` `range` `(` `1` `, ` `10` `):` ` ` `# If any pair is obtained` ` ` `# with difference x / 99` ` ` `if` `((i ` `-` `j) ` `=` `=` `diff):` ` ` `# Increase count` ` ` `ans ` `+` `=` `10` `;` ` ` `# Return the count` ` ` `return` `ans;` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` ` ` `x ` `=` `792` `;` ` ` `print` `(Count_Number(x));` `# This code is contributed by shikhasingrajput` |

## C#

`// C# program to implement` `// the above approach ` `using` `System;` `class` `GFG{` ` ` `// Function to count three-digit` `// numbers having difference x` `// with its reverse` `static` `int` `Count_Number(` `int` `x)` `{` ` ` `int` `ans = 0;` ` ` ` ` `// If x is not multiple of 99` ` ` `if` `(x % 99 != 0)` ` ` `{` ` ` ` ` `// No solution exists` ` ` `ans = -1;` ` ` `}` ` ` `else` ` ` `{` ` ` `int` `diff = x / 99;` ` ` ` ` `// Generate all possible pairs` ` ` `// of digits [1, 9]` ` ` `for` `(` `int` `i = 1; i < 10; i++)` ` ` `{` ` ` `for` `(` `int` `j = 1; j < 10; j++)` ` ` `{` ` ` ` ` `// If any pair is obtained` ` ` `// with difference x / 99` ` ` `if` `((i - j) == diff)` ` ` `{` ` ` ` ` `// Increase count` ` ` `ans += 10;` ` ` `}` ` ` `}` ` ` `}` ` ` `}` ` ` ` ` `// Return the count` ` ` `return` `ans;` `}` ` ` `// Driver Code` `public` `static` `void` `Main()` `{` ` ` `int` `x = 792;` ` ` ` ` `Console.WriteLine(Count_Number(x));` `}` `}` `// This code is contributed by code_hunt` |

## Javascript

`<script>` `// Javascript program to implement` `// the above approach` `// Function to count three-digit` `// numbers having difference x` `// with its reverse` `function` `Count_Number(x)` `{` ` ` `let ans = 0;` ` ` ` ` `// If x is not multiple of 99` ` ` `if` `(x % 99 != 0)` ` ` `{` ` ` ` ` `// No solution exists` ` ` `ans = -1;` ` ` `}` ` ` `else` ` ` `{` ` ` `let diff = x / 99;` ` ` ` ` `// Generate all possible pairs` ` ` `// of digits [1, 9]` ` ` `for` `(let i = 1; i < 10; i++)` ` ` `{` ` ` `for` `(let j = 1; j < 10; j++)` ` ` `{` ` ` ` ` `// If any pair is obtained` ` ` `// with difference x / 99` ` ` `if` `((i - j) == diff)` ` ` `{` ` ` ` ` `// Increase count` ` ` `ans += 10;` ` ` `}` ` ` `}` ` ` `}` ` ` `}` ` ` ` ` `// Return the count` ` ` `return` `ans;` `}` `// Driver code` `let x = 792;` ` ` `document.write(Count_Number(x));` `// This code is contributed by splevel62` `</script>` |

**Output**

10

**Time Complexity:** O(1)**Auxiliary Space:** O(1)

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