Question 1: 
Number game between user and computer. The user starts by entering either 1 or 2 or 3 digits starting from 1 sequentially. The computer can return either 1 or 2 or 3 next digits in sequence, starting from the max number played by the user. User enters the next 1 or 2 or 3 next digits in sequence, starting from the max number played by the computer. Whoever reaches 20 first wins the game.
Note: 
- the numbers should be in sequence starting from 1.
- minimum number user or computer should pick is at least 1 digit in sequence
- maximum number user or computer can pick only 3 digits in sequence

import random

def gettinginput(maxnum):
    while True:
        userinput = input("Player : ")
        numbers = list(map(int, userinput.split()))
        if all(num in range(maxnum, maxnum + 4) for num in numbers) and 1 <= len(numbers) <= 3:
            return numbers
        print("Invalid input. Please try again.")

def computerinput(maxnum):
    numtoplay = random.randint(1, 3)
    numbers = list(range(maxnum, maxnum + numtoplay))
    print(f"Computer played: {numbers}")
    return numbers

def main():
    maxnum = 1

    while maxnum <= 20:
        usernum = gettinginput(maxnum)
        maxnum += len(usernum)

        if maxnum >= 20:
            print("Player Wins!!!")
            break
        
        computernum = computerinput(maxnum)
        maxnum += len(computernum)

        if maxnum >= 20:
            print("Computer Wins!!!")
            break

main()

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QUESTION 2:
Develop a function called ncr(n,r) which computes r-combinations of n-distinct object . use this function to print pascal triangle, where number of rows is the input
def ncr(n, r):
    if r > n or r < 0:
        return 0
    return factorial(n) // (factorial(r) * factorial(n - r))
    
def factorial(n):
    if n == 0 or n == 1:
        return 1
    result = 1
    for i in range(2, n + 1):
        result *= i
    return result
    
def print_pascal_triangle(rows):
    for i in range(rows):
        for j in range(i + 1):
            print(ncr(i, j), end=' ')
        print()

rows = int(input("Enter the number of rows for Pascal's triangle: "))
print_pascal_triangle(rows)
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QUESTION 3:
Read a list of n numbers during runtime. Write a Python program to print the repeated elements with frequency count in a list.
def count_frequencies(numbers):
    frequency = {}
    for num in numbers:
        if num in frequency:
            frequency[num] += 1
        else:
            frequency[num] = 1
    return frequency

def print_repeated_elements(frequency):
    for num, count in frequency.items():
        print(f"Element {num} has come {count} times")

n = int(input("Enter the number of elements: "))
numbers = []
print("Enter the numbers :")
for _ in range(n):
    number = int(input())
    numbers.append(number)

frequency = count_frequencies(numbers)
print_repeated_elements(frequency)

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QUESTION 4:
Develop a python code to read matric A of order 2X2 and Matrix B of order 2X2 from a file and perform the addition of Matrices A & B and Print the results

with open("matrices,txt", 'r') as file:
    lines = file.readlines()
    A = [[int(num) for num in lines[0].strip().split()],
         [int(num) for num in lines[1].strip().split()]]
    B = [[int(num) for num in lines[2].strip().split()],
        [int(num) for num in lines[3].strip().split()]]

def add_matrices(A, B):
    return [[A[0][0] + B[0][0], A[0][1] + B[0][1]],
            [A[1][0] + B[1][0], A[1][1] + B[1][1]]]

def print_matrix(matrix):
    for row in matrix:
        print(" ".join(map(str, row)))

filename = 'matrices.txt'
A, B = read_matrices(filename)
result = add_matrices(A, B)
print("Result of A + B:")
print_matrix(result)
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QUESTION 5:
Write a program that overloads the + operator so that it can add two objects of the class Fraction.
Fraction can be considered of the for P/Q where P is the numerator and Q is the denominator

class Fraction:
    def __init__(self, numerator, denominator):
        if denominator == 0:
            raise ValueError("Denominator cannot be zero.")
        self.numerator = numerator
        self.denominator = denominator
        self.simplify()

    def simplify(self):
        def gcd(a, b):
            while b:
                a, b = b, a % b
            return abs(a)

        common_divisor = gcd(self.numerator, self.denominator)
        self.numerator //= common_divisor
        self.denominator //= common_divisor
        if self.denominator < 0:
            self.numerator = -self.numerator
            self.denominator = -self.denominator

    def __add__(self, other):
        if not isinstance(other, Fraction):
            return NotImplemented
        
        new_numerator = (self.numerator * other.denominator) + (other.numerator * self.denominator)
        new_denominator = self.denominator * other.denominator
        
        return Fraction(new_numerator, new_denominator)

f1 = Fraction(1, 2)
f2 = Fraction(1, 4)
result = f1 + f2
print(f"{result.numerator}/{result.denominator}")