# Third last digit in 5^N for given N

Given a positive integer N. The task is to find the value of 3rd digit from last (right-most) of 5N.

Examples:

```Input : N = 6
Output : 6
Explanation : Value of 56 = 15625.

Input : N = 3
Output : 1
Explanation : Value of 53 = 125.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach : Before moving to actual approach, some facts regarding number theory are listed below as:

• 53 is the smallest 3 digit number which is power of 5.
• As 125 * 5 = 625, this conclude that multiple of number (ending with 125) with 5 always construct 625 as last three digit of result.
• Again as, 625 * 5 = 3125, this conclude that multiple of number (ending with 625) with 5 always construct 125 as last three digit of result.

Hence, the final general solution is :

case 1: if n < 3, answer = 0.
case 2: if n >= 3 and is even , answer = 6.
case 3: if n >= 3 and is odd , answer = 1.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to find the element ` `int` `findThirdDigit(``int` `n) ` `{ ` `    ``// if n < 3 ` `    ``if` `(n < 3) ` `        ``return` `0; ` ` `  `    ``// If n is even return 6 ` `    ``// If n is odd return 1 ` `    ``return` `n & 1 ? 1 : 6; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 7; ` ` `  `    ``cout << findThirdDigit(n); ` `  `  `    ``return` `0; ` `}  `

## Java

 `// Java implementation of the  ` `// above approach ` `class` `GFG ` `{ ` `     `  `// Function to find the element ` `static` `int` `findThirdDigit(``int` `n) ` `{ ` `    ``// if n < 3 ` `    ``if` `(n < ``3``) ` `        ``return` `0``; ` ` `  `    ``// If n is even return 6 ` `    ``// If n is odd return 1 ` `    ``return` `(n & ``1``) > ``0` `? ``1` `: ``6``; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String args[]) ` `{ ` `    ``int` `n = ``7``; ` ` `  `    ``System.out.println(findThirdDigit(n)); ` `}  ` `} ` ` `  `// This code is contributed  ` `// by Akanksha Rai `

## Python3

 `# Python3 implementation of the  ` `# above approach ` ` `  `# Function to find the element ` `def` `findThirdDigit(n): ` ` `  `    ``# if n < 3 ` `    ``if` `n < ``3``: ` `        ``return` `0` ` `  `    ``# If n is even return 6 ` `    ``# If n is odd return 1 ` `    ``return` `1` `if` `n ``and` `1` `else` `6` ` `  `# Driver code ` `n ``=` `7` `print``(findThirdDigit(n)) ` ` `  `# This code is contributed  ` `# by Shrikant13 `

## C#

 `// C# implementation of the above approach ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `// Function to find the element ` `static` `int` `findThirdDigit(``int` `n) ` `{ ` `    ``// if n < 3 ` `    ``if` `(n < 3) ` `        ``return` `0; ` ` `  `    ``// If n is even return 6 ` `    ``// If n is odd return 1 ` `    ``return` `(n & 1)>0 ? 1 : 6; ` `} ` ` `  `// Driver code ` `static` `void` `Main() ` `{ ` `    ``int` `n = 7; ` ` `  `    ``Console.WriteLine(findThirdDigit(n)); ` `}  ` `} ` ` `  `// This code is contributed by mits `

## PHP

 ` `

Output:

```1
```

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