def left_ordered_fraction(in_fraction, max_d):
"""Return the numerator and denominator of the reduced fraction immediately below in_fraction in an ordered list
of fractions with d <= max_d.
:param in_fraction: reference fraction in the form (numerator, denominator)
:param max_d: maximum denominator to check
:return: reduced proper fraction of the form (numerator, denominator)
"""
in_fraction = (in_fraction[0]/in_fraction[1], (in_fraction[0], in_fraction[1]))
min_delta = (in_fraction[0], (0, 0))
# Loop through all denominators checking just the fraction to the left of in_fraction
for d in range(2, max_d+1):
n = int(d * in_fraction[0])
fraction = n/d
delta = in_fraction[0] - fraction
if 0.0 < delta < min_delta[0]:
min_delta = (delta, (n, d))
return common.reduce_fraction(min_delta[1][0], min_delta[1][1])
print(coin_combinations(200, [200, 100, 50, 20, 10, 5, 2, 1], 1))
print(coin_combinations(1, [200, 100, 50, 20, 10, 5, 2, 1], 1))
elif problem_num == 32:
print(is_pandigital_3(39, 186, 39*186))
print(pandigital_products())
print(sum(pandigital_products()))
elif problem_num == 33:
print()
zfraction_list = digit_canceling_fractions()
num_product = 1
den_product = 1
for fraction in zfraction_list:
num_product *= fraction[0]
den_product *= fraction[1]
print(zfraction_list)
print(common.reduce_fraction(num_product, den_product))
elif problem_num == 34:
print()
print(factorial_sum_list(200))
print(factorial_sum_list())
elif problem_num == 35:
print(circular_primes(100))
print(len(circular_primes(1000000)))
elif problem_num == 36:
print(double_base_palindromes(1000))
print(double_base_palindromes(1000000))
elif problem_num == 37:
prime_list_10M = common.sieve_erathosthenes(10000000)
print(next_right_extend_prime('379', prime_list_10M))
print(next_left_extend_prime('797', prime_list_10M))
print(truncatable_primes())