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.

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++

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// C++ implementation of the above approach
  
#include <bits/stdc++.h>
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;

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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PHP

Output:

1


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