# 21 Matchsticks Problem

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

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

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); ` ` `  `    ``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 `

Output:

```2 1 3 3
```

Time Complexity: O(N)

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