# Count Numbers with N digits which consists of even number of 0’s

Given a number **N**. The task is to find the count of numbers which have N digits and even number of zeroes.

**Note: **The number can have preceding 0’s.

**Examples**:

Input: N = 2Output: Count = 81 Total 2 digit numbers are 99 considering 1 as 01. 2 digit numbers are 01, 02, 03, 04, 05.... 99 Numbers with odd 0's are 01, 02, 03, 04, 05, 06, 07, 08, 09 10, 20, 30, 40, 50, 70, 80, 90 i.e. 18 The rest of the numbers between 01 and 99 will do not have any zeroes and zero is also an even number. So, numbers with even 0's are 99 - 18 = 81.Input: N = 3Output: Count = 755

**Approach:** The idea is to find the Count Numbers with N digits which consists of odd number of 0’s and subtract it from the total number with N digits to get the number with even 0’s.

## C++

`// C++ program to count numbers with N digits ` `// which consists of odd number of 0's ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to count Numbers with N digits ` `// which consists of odd number of 0's ` `int` `countNumbers(` `int` `N) ` `{ ` ` ` `return` `(` `pow` `(10, N) - 1) - (` `pow` `(10, N) - ` `pow` `(8, N)) / 2; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `n = 2; ` ` ` ` ` `cout << countNumbers(n) << endl; ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to count numbers ` `// with N digits which consists ` `// of odd number of 0's ` `import` `java.lang.*; ` `import` `java.util.*; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to count Numbers with ` `// N digits which consists of odd ` `// number of 0's ` `static` `double` `countNumbers(` `int` `N) ` `{ ` ` ` `return` `(Math.pow(` `10` `, N) - ` `1` `) - ` ` ` `(Math.pow(` `10` `, N) - ` ` ` `Math.pow(` `8` `, N)) / ` `2` `; ` `} ` ` ` `// Driver code ` `static` `public` `void` `main (String args[]) ` `{ ` ` ` `int` `n = ` `2` `; ` ` ` `System.out.println(countNumbers(n)); ` `} ` `} ` ` ` `// This code si contributed ` `// by Akanksha Rai ` |

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## Python3

`# Python3 program to count numbers with N digits ` `# which consists of odd number of 0's ` ` ` `# Function to count Numbers with N digits ` `# which consists of odd number of 0's ` `def` `countNumber(n): ` ` ` ` ` `return` `(` `pow` `(` `10` `,n)` `-` `1` `)` `-` `(` `pow` `(` `10` `,n)` `-` `pow` `(` `8` `,n))` `/` `/` `2` ` ` ` ` `# Driver code ` `n ` `=` `2` `print` `(countNumber(n)) ` ` ` `# This code is contributed by Shrikant13 ` |

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## C#

`// C# program to count numbers ` `// with N digits which consists ` `// of odd number of 0's ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to count Numbers with ` `// N digits which consists of odd ` `// number of 0's ` `static` `double` `countNumbers(` `int` `N) ` `{ ` ` ` `return` `(Math.Pow(10, N) - 1) - ` ` ` `(Math.Pow(10, N) - ` ` ` `Math.Pow(8, N)) / 2; ` `} ` ` ` `// Driver code ` `static` `public` `void` `Main () ` `{ ` ` ` `int` `n = 2; ` ` ` `Console.WriteLine(countNumbers(n)); ` `} ` `} ` ` ` `// This code si contributed by ajit ` |

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## PHP

`<?php ` `// PHP program to count numbers with N digits ` `// which consists of odd number of 0's ` ` ` `// Function to count Numbers with N digits ` `// which consists of odd number of 0's ` `function` `countNumbers(` `$N` `) ` `{ ` ` ` `return` `(pow(10, ` `$N` `) - 1) - ` ` ` `(pow(10, ` `$N` `) - pow(8, ` `$N` `)) / 2; ` `} ` ` ` `// Driver code ` `$n` `= 2; ` `echo` `countNumbers(` `$n` `),` `"\n"` `; ` ` ` `// This code is contributed by akt_mit ` `?> ` |

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**Output:**

81

**Note**: Answer can be very large, so for N greater than 9, use modular exponentiation.

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