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21 Matchsticks Problem
  • Difficulty Level : Medium
  • Last Updated : 26 Apr, 2021

Given 21 Matchsticks and 2 users, A and B (computer and user respectively). Users can pick matchsticks not more than four at a time. The one who is forced to pick the last matchstick loses. 
Given an array arr[] which contains the moves of the computer. The task is to print the moves of the user so that the user wins the game.
Examples
 

Input : N = 4, arr=[ 3, 4, 2, 2] 
Output : 2, 1, 3, 3 
When the computer chooses 3 sticks, the user chooses 2 sticks 
When the computer chooses 4 sticks, the user chooses 1 stick 
When the computer chooses 2 sticks, the user chooses 3 sticks 
When the computer chooses 2 sticks, the user chooses 3 sticks 
Now only 1 stick is left and the computer is forced to pick that stick 
Hence the user wins the game.
Input : N = 4 arr=[ 1, 1, 4, 3] 
Output : 4, 4, 1, 2 
 

 

Approach: 
 

  • Idea is to think for 20 matchsticks as the user who would pick the last one will lose the game.
  • Divide 20 into four parts that is, each part is of size 5. So if the computer picks x matchsticks then the user should pick (5-x) matchsticks and should proceed in the same way.
  • In this way, 20 matchsticks will be used and the last matchstick would be picked by the computer.

 



Below is the implementation of the above approach 
 

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the optimal strategy
void TwentyoneMatchstick(int arr[], int N)
{
 
    // Removing matchsticks in blocks of five
    for (int i = 0; i < N; i += 1) {
        cout << 5 - arr[i] << " ";
    }
    cout << endl;
}
 
// Driver code
int main()
{
    int arr[] = { 3, 4, 2, 2 };
 
    int N = sizeof(arr) / sizeof(arr[0]);
 
    TwentyoneMatchstick(arr, N);
 
    return 0;
}

Java




// Java implementation of the approach
class GFG
{
 
// Function to return the optimal strategy
static void TwentyoneMatchstick(int arr[], int N)
{
 
    // Removing matchsticks in blocks of five
    for (int i = 0; i < N; i += 1)
    {
        System.out.print(5 - arr[i] + " ");
    }
    System.out.println();
}
 
// Driver code
public static void main(String[] args)
{
    int arr[] = {3, 4, 2, 2};
 
    int N = arr.length;
 
    TwentyoneMatchstick(arr, N);
}
}
 
// This code is contributed by Princi Singh

Python3




# Python3 implementation of the approach
 
# Function to return the optimal strategy
def TwentyoneMatchstick(arr, N):
 
    # Removing matchsticks in blocks of five
    for i in range(N):
        print(5 - arr[i], end = " ")
 
# Driver code
arr = [3, 4, 2, 2 ]
 
N = len(arr)
 
TwentyoneMatchstick(arr, N)
 
# This code is contributed
# by Mohit Kumar

C#




// C# implementation of the approach
using System;
 
class GFG
{
 
// Function to return the optimal strategy
static void TwentyoneMatchstick(int []arr, int N)
{
 
    // Removing matchsticks in blocks of five
    for (int i = 0; i < N; i += 1)
    {
        Console.Write(5 - arr[i] + " ");
    }
    Console.Write("\n");
}
 
// Driver code
public static void Main(String[] args)
{
    int []arr = {3, 4, 2, 2};
 
    int N = arr.Length;
 
    TwentyoneMatchstick(arr, N);
}
}
 
// This code is contributed by Princi Singh

Javascript




// javascript implementation of the approach
   
// Function to return the optimal strategy
 function TwentyoneMatchstick(arr, N)
{
   
    // Removing matchsticks in blocks of five
    for (var i = 0; i < N; i += 1)
    {
        document.write(5 - arr[i] + " ");
    }
    document.write("<br>");
}
   
// Driver code
    var arr = [3, 4, 2, 2];
    var N = arr.length;
    TwentyoneMatchstick(arr, N);
 
// This code is contributed by bunnyram19.
  
Output: 
2 1 3 3

 

Time Complexity: O(N)
 

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