Problem statement: Next week's winning lottery numbers are 8 different numbers all in the range 11 to 99 inclusiveThree, and only three of them are prime numbers and the sum of these three is 265Of the other 5, just two of them are even, and when these 2 are multiplied together they make 1332The mean of the remaining 3 is 23What are the eight wi…

winnin_lottery_number.py

"""
Problem statement: Next week's winning lottery numbers are 8 different numbers all in the range 11 to 99 inclusive
Three, and only three of them are prime numbers and the sum of these three is 265
Of the other 5, just two of them are even, and when these 2 are multiplied together they make 1332
The mean of the remaining 3 is 23
What are the eight winning lottery numbers?
"""

# (x + y + z) == 265  and all((is_prime(num) for num in (x, y, z)))
# all((is_even(num) for num in (p, q))) and p * q == 1332
# mean((a, b, c)) == 23
from typing import Iterable
from itertools import combinations
from statistics import mean
import math


def is_prime(number):
    if number < 2:
        return False
    if number == 2:
        return True
    for num in range(2, int(math.sqrt(number))+1):
        if number % num == 0:
            return False
    return True


def is_even(number):
    return number % 2 == 0


def check_not_condition(numbers: Iterable[int]):
    """
    Not condition ensures, that:
    - only 3 numbers are prime
    - only 2 numbers are even
    
    :param numbers:
    :return:
    """
    prime_count = [1 for num in numbers if is_prime(num)].count(1)
    even_count = [1 for num in numbers if is_even(num)].count(1)
    
    return prime_count == 3 and even_count == 2


def solve():
    # get all the combinations of 3 prime numbers
    prime_numbers = [num for num in range(11, 100) if is_prime(num)]
    even_numbers = [num for num in range(11, 100) if is_even(num)]
    prime_combinations = combinations(prime_numbers, 3)
    
    _possible_prime_numbers = []
    for x, y, z in prime_combinations:
        if (x + y + z) == 265:
            _possible_prime_numbers.append((x, y, z))
    
    _possible_five_numbers = []
    for x, y, z in _possible_prime_numbers:
        
        # get all the combinations of 2 even numbers
        even_combinations = combinations(even_numbers, 2)
        for p, q in even_combinations:
            if all((is_even(num) for num in (p, q))) and p * q == 1332:
                _possible_five_numbers.append((x, y, z, p, q))
    
    for x, y, z, p, q in _possible_five_numbers:
        
        # get all the combinations of 3 numbers whose mean is 23
        remaining_numbers = [num for num in range(11, 100) if num not in (x, y, z, p, q)]
        remaining_combinations = combinations(remaining_numbers, 3)
        for a, b, c in remaining_combinations:
            if mean((a, b, c)) == 23 and check_not_condition((x, y, z, p, q, a, b, c)):
                return x, y, z, p, q, a, b, c


if __name__ == '__main__':
    res = solve()
    print(res)