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

• Difficulty Level : Easy
• Last Updated : 15 Sep, 2022

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 = 2
Output: 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 = 3
Output: 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 ``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;``}`

## 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 is contributed``// by Akanksha Rai`

## 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`

## 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 is contributed by ajit`

## PHP

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## Javascript

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Output:

`81`

Time Complexity: O(logN), since the pow function takes (log N) times to find the power to base N.

Auxiliary Space: O(1), since no extra space has been taken.

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

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