def main() -> None:
print("Problem 21")
with measure_execution_time("old"):
result = all_amicable_numbers_under(LIMIT)
with measure_execution_time("new"):
divisor_sums = create_divisor_sums(30_000)
result2 = sum(all_amicable_numbers_under_fast(LIMIT, divisor_sums))
assert result == result2
print(f"The sum of all the amicable numbers under {LIMIT} is {result}")
def main():
print("Problem 9")
with measure_execution_time():
a, b, c = find_pythagorean_triplet_summing_up_to(1000)
print(
f"The Pythagorean triplet for which a + b + c = 1000 is {a}, {b}, {c}")
print(f"The product for which is {a*b*c}")
def main() -> None:
print("Problem 23")
with measure_execution_time():
result = sum(integers_not_sum_abundant(LIMIT))
print(
f"the sum of all the positive integers which cannot be written as the sum of two abundant numbers is {result}"
)
def main():
print("Problem 26")
with measure_execution_time():
result = value_with_longest_recurring_cycle(LIMIT)
print(
f"The value of d < {LIMIT} for which 1/d contains the longest recurring cycle in its decimal fraction part is {result}"
)
def main():
n = 600_851_475_143
with measure_execution_time():
prime_factors = calc_prime_factors(n)
print("Problem 3")
print("the largest prime factor of the number {} = {}".format(
n, max(prime_factors)))
def main():
print("Problem 25")
with measure_execution_time():
result = fibonacci_index(NR_DIGITS)
print(
f"The index of the first term in the Fibonacci sequence to contain {NR_DIGITS} digits is {result}"
)
def main():
print("Problem 13")
with measure_execution_time():
numbers = [int(n) for n in NUMBERS_STRING.split('\n')]
digits = str(sum(numbers))[:10]
print(
f"The first 10 digits of the sum of 100 50-digit numbers is {digits}")
def main():
limit = 4_000_000
with measure_execution_time():
even_fibonacci = (n for n in fibonacci_sequence(limit) if is_even(n))
result = sum(even_fibonacci)
print("Problem 2")
print(f"The sum of all even fibonacci numbers below {limit} = {result}")
def main() -> None:
print("Problem 4")
digits = 3
with measure_execution_time():
result = max(largest_palindrome(digits))
print(f"The largest palindrome of the product of two {digits}-digit \
numbers is {result}")
def main():
print("Problem 27")
with measure_execution_time():
result = product_of_coefficients()
print(
f"The product of a and b for the quadric expression with maximum number of primes is {result}"
)
def main():
print("Problem 28")
with measure_execution_time():
result = sum_of_spiral_diagonals(LIMIT)
print(
f"The sum of the numbers on the diagonals of a {LIMIT} by {LIMIT} spiral is {result}"
)
def main():
print("Problem 5")
limit = 20
with measure_execution_time():
result = smallest_evenly_divisible_number(limit)
print(
f"The smallest positive number that is evenly divisible by all of the numbers from 1 to {limit} is {result}."
)
def main() -> None:
print("Problem 6")
limit = 1_000
with measure_execution_time():
result = square_of_sum(limit) - sum_of_squares(limit)
print(
f'The difference between the sum of squares and the square of the sum for the first {limit} natural numbers is {result}'
)
def main():
print('Problem 22')
with measure_execution_time():
with open('../resources/p022_names.txt', 'r',
encoding='ascii') as file:
name_list = file.readline().replace('"', '').split(',')
result = sum(name_scores(name_list))
print(f'The total of all name scores in the file is {result}')
def main() -> None:
print("Problem 19")
with measure_execution_time():
start_year = 1901
end_year = 2001
result = sundays_on_day_of_month(1, start_year, end_year)
print(
f"There are {result} Sundays on the first of the month between {start_year} and {end_year}"
)
def main():
print("Problem 7")
with measure_execution_time():
product, adjacent_digits = adjacent_digits_with_highest_product(
LIMIT, [int(s) for s in BIG_NUMBER])
string = "".join(str(s) for s in adjacent_digits)
print(
f"The {LIMIT} adjacent digits with highest product is {string}, the product of which is {product}."
)
def main():
print("Problem 12")
n = 0
divisors = 0
with measure_execution_time():
while divisors <= LIMIT:
n += 1
divisors = calc_divisors(triangle_number(n))
print(f"The first triangle number with over {LIMIT} divisors is {triangle_number(n)}")
def main():
print("Problem 24")
with measure_execution_time():
nth_permutation_iterator = islice(permutations(range(10)), LIMIT - 1,
LIMIT)
nth_permutation = list(nth_permutation_iterator)[0]
result = ''.join(str(d) for d in nth_permutation)
print(
f"The {LIMIT}th lexicographic permutation of the digits 0 to 9 is {result}"
)
def main() -> None:
print("Problem 17")
with measure_execution_time():
words = [
three_digit_number_written_as_word(n) for n in range(1, LIMIT)
]
cleaned_words = [clean_word(word) for word in words]
result = sum(len(w) for w in cleaned_words) + len("onethousand")
print(
f"the number of letters used to write 1 to {LIMIT} in words is {result}"
)
def main():
print("Problem 14")
with measure_execution_time():
longest = 0
result = 0
chain_length_dict = dict()
for n in range(1_000_000):
chain = length_of_chain(n, chain_length_dict)
if chain > longest:
longest = chain
result = n
def main() -> None:
print("Problem 7")
with measure_execution_time():
result = n_th_prime_number(LIMIT)
print(f'The {LIMIT}st prime number is {result}')
def main() -> None:
print("Problem 20")
with measure_execution_time():
result = sum(int(char) for char in str(math.factorial(NUMBER)))
print(f"The sum of digits in the number {NUMBER}! is {result}")
divider()
problem_020.main()
divider()
problem_021.main()
divider()
problem_022.main()
divider()
problem_023.main()
divider()
problem_024.main()
divider()
problem_025.main()
divider()
problem_026.main()
divider()
problem_027.main()
divider()
problem_028.main()
divider()
problem_029.main()
divider()
problem_030.main()
divider()
problem_067.main()
divider()
if __name__ == '__main__':
with measure_execution_time("Time for all problems together"):
main()
def main():
print("Problem 11")
with measure_execution_time():
result = greatest_product_adjacent_numbers(LIMIT)
print(f"the greatest product of {LIMIT} adjacent numbers in the same direction in the 20×20 grid is {result}")
def main():
print("Problem 30")
with measure_execution_time():
result = sum_numbers_that_are_sum_of_fifth_powers_of_their_digits()
print(f"the sum of all the numbers that can be written as the sum of fifth powers of their digits is {result}")
def main() -> None:
print("Problem 67")
with measure_execution_time():
result = find_longest_path_triangle(get_triangle_from_file())
print(f"The maximum total from top to bottom of the triangle is {result}")
def main():
print("Problem 10")
with measure_execution_time():
result = np.sum(sieve_of_eratosthenes(LIMIT))
print(f"The sum of all primes below {LIMIT:,} is {result:,}.")
def main():
print("Problem 16")
with measure_execution_time():
result = sum([int(s) for s in str(2**1000)])
print(f"the sum of the digits of the number 2^1000 is {result}")
def main():
print("Problem 15")
with measure_execution_time():
# we add 1 to size as a NxN grid has N+1xN+1 intersecetions.
result = nr_routes_in_grid(SIZE + 1)
print(f"the number of routes through a {SIZE}x{SIZE} grid = {result}")
def main():
print("Problem 29")
with measure_execution_time():
result = nr_distinct_terms(LIMIT)
print(f"The number of distinct terms with a and b =< {LIMIT} is {result}")
