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0x0A-primegame/README.md

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+# Prime Game Winner Determination
+
+## Overview
+
+This project implements an algorithm to determine the winner of a prime number game played between Maria and Ben. The game involves selecting prime numbers from a set of consecutive integers and removing their multiples. Maria always goes first, and both players play optimally.
+
+## Algorithm Description
+
+### Sieve of Eratosthenes
+
+The core of the algorithm relies on the Sieve of Eratosthenes to efficiently identify prime numbers up to the maximum value in the given rounds. This method marks non-prime numbers by iterating through and eliminating the multiples of each prime starting from 2.
+
+### Game Simulation
+
+For each round:
+1. Initialize the set of numbers from 1 to `n`.
+2. Maria starts by choosing the smallest prime and removing it along with its multiples.
+3. Ben follows by choosing the next available prime and removing it along with its multiples.
+4. The game continues until no more primes can be chosen.
+
+The player who cannot make a move loses the game. The algorithm tracks the number of moves and determines the winner based on the parity (odd or even) of the number of moves.
+
+## Why This Algorithm?
+
+1. **Efficiency:** The Sieve of Eratosthenes is an efficient algorithm for finding all prime numbers up to a given limit, which is crucial for handling the upper constraints of the problem.
+2. **Optimal Play Simulation:** The game simulation ensures that both players play optimally, which is essential for accurately determining the winner.
+3. **Clarity:** The use of helper functions and detailed documentation provides clear understanding and maintenance of the code.
+
+## Usage
+
+To determine the winner for a set of rounds, use the `isWinner` function:
+
+```python
+print("Winner:", isWinner(5, [2, 5, 1, 4, 3]))  # Output: "Ben"
+```
+
+The function takes the number of rounds `x` and a list `nums` containing the values of `n` for each round. It returns the name of the player who won the most rounds or `None` if there is no clear winner.