def main(verbose=False):
result = []
# We have at most 7 digits, so we consider all ascending
# lists of digits with a digit sum between 1 and 63.
# Since ascending requires the first element of the digit lists
# is *equal to* the minimum, we allow an 8th digit which is
# simply a padded zero
for digit_sum in range(1, 63 + 1):
for choice in ascending(8, digit_sum, 0, 9):
choice = choice[1:]
non_zero = [digit for digit in choice if digit != 0]
factorial_sum = sum(factorial(digit) for digit in non_zero)
possible_zeros = 7 - len(non_zero)
# Can fill out the number with zeros (up to 7 digits)
for zeros_add in range(possible_zeros + 1):
factorial_digits = [int(digit) for digit in str(factorial_sum)]
if (sorted(factorial_digits) ==
sorted(non_zero + [0] * zeros_add)):
result.append(factorial_sum)
factorial_sum += 1 # Add factorial(0)
result = [val for val in result if val not in [1, 2]]
if verbose:
return "%s.\nThe full list of numbers is as follows: %s." % (
sum(result), ", ".join(str(number) for number in result))
else:
return sum(result)
def dice_outcomes(num_dice, num_sides):
result = {}
for bottom in range(1, num_sides + 1):
for dice_sum in range(1 * num_dice, num_sides * num_dice + 1):
for outcome in ascending(num_dice, dice_sum, bottom, num_sides):
curr_sum = sum(outcome)
# if curr_sum is not in result, sets to total_perms(outcome)
# (default 0 returned by get)
result[curr_sum] = (result.get(curr_sum, 0) +
total_perms(outcome))
return result
def main(verbose=False):
MATCHES = []
for bottom in range(1, 12 + 1):
MATCHES.extend(ascending(10, 70, bottom, 12))
add_ons = {}
for biggest in range(1, 8):
add_ons[biggest] = generate_addons(10, 1, biggest)
count = 0
for match in MATCHES:
bottom = match[0]
for addon in add_ons[bottom]:
curr = addon + match
count += total_perms(curr)
return count