# 21 Matchsticks Problem

• Difficulty Level : Medium
• Last Updated : 22 Sep, 2022

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 ` `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(``"
"``);` `}` `  `  `// 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)
Auxiliary Space: O(1)

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