# 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; ` `} ` |

*chevron_right*

*filter_none*

## 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 ` |

*chevron_right*

*filter_none*

## 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 ` |

*chevron_right*

*filter_none*

## 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 ` |

*chevron_right*

*filter_none*

## 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 ` `?> ` |

*chevron_right*

*filter_none*

**Output:**

81

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

## Recommended Posts:

- Count Numbers with N digits which consists of odd number of 0's
- Count of numbers between range having only non-zero digits whose sum of digits is N and number is divisible by M
- Count of Numbers such that difference between the number and sum of its digits not less than L
- Count of Numbers in Range where the number does not contain more than K non zero digits
- Count the number of digits of palindrome numbers in an array
- Count of numbers whose sum of increasing powers of digits is equal to the number itself
- Count total number of N digit numbers such that the difference between sum of even and odd digits is 1
- Smallest multiple of 3 which consists of three given non-zero digits
- Count numbers in given range such that sum of even digits is greater than sum of odd digits
- Count of integers in a range which have even number of odd digits and odd number of even digits
- Count numbers with same first and last digits
- Count of numbers from range [L, R] whose sum of digits is Y
- Count of numbers from range [L, R] that end with any of the given digits
- Count numbers less than N containing digits from the given set : Digit DP
- Count of n digit numbers whose sum of digits equals to given sum

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.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.