def generate_rotated_numbers(list):
if len(list) > 0:
permutations = [list_as_number(list)]
for i in range(1,len(list)):
number = list_as_number(rotate_list_left(list,i))
permutations.append(number)
return permutations
else:
return []
def check_rotational_prime(list):
number = list_as_number(list)
if len(list) > 0:
checked_dict[number] = True
if check_primality_dyn(number,upper_bound):
for i in range(1,len(list)):
number = list_as_number(rotate_list_left(list,i))
checked_dict[number] = True
if not check_primality_dyn(number,upper_bound):
return False
return True
else:
return False
else:
return False
def main():
primes_list = [2, 3, 5, 7, 11, 13, 17]
permutations_list = get_digit_permutations_as_list(1234567890)
sum = 0
for permutation in permutations_list:
number = list_as_number(permutation)
try:
for i in range(1, len(permutation) - 2):
if list_as_number(permutation[i : i + 3]) % primes_list[i - 1] != 0:
raise Found
print "found one!", number
sum += number
except Found:
pass
print "Sum: ", sum
if __name__ == '__main__':
keylog = [319,680,180,690,129,620,762,689,762,318,368,710,720,710,629,168,\
160,689,716,731,736,729,316,729,729,710,769,290,719,680,318,389,162,289,162,\
718,729,319,790,680,890,362,319,760,316,729,380,319,728,716]
key = []
try:
while(True):
fixed = len(keylog)
for attempt in keylog:
list = number_as_list(attempt)
index = [-1,-1,-1]
for d in range(0,len(list)):
digit = list[d]
if key.count(digit) == 0:
key.append(digit)
index[d] = key.index(digit)
else:
index[d] = key.index(digit)
for i in range(1,len(list)):
if index[i] < index[i-1]:
digit = list[i]
key.remove(digit)
key.insert(index[i-1],digit)
fixed -= 1
if fixed == len(keylog): raise Found
except Found:
print "Shortest key: ", list_as_number(key)
exit(0)
#!python
from pelib import number_as_list, list_as_number
from pelib import check_1_9_pandigital as check_pandigital
if __name__ == '__main__':
best_starting_number = -1
best_pandigital = -1
number = 9876
while(number > 0):
number -= 1
list = number_as_list(number)
factor = 2
while(len(list) < 9):
list += number_as_list(number*factor)
factor += 1
if check_pandigital(list) and factor >= 3:
pand_number = list_as_number(list)
if pand_number > best_pandigital:
best_pandigital = pand_number
best_starting_number = number
print "Largest pandigital: ", best_pandigital
exit(0)
numer_matches = []
denom_matches = []
for numer in range(lower_bound,upper_bound):
for denom in range(lower_bound,upper_bound):
if numer < denom:
# fractions under consideration are all less than 1
numer_list = number_as_list(numer)
denom_list = number_as_list(denom)
for digit in range(1,10):
# skipping over removing zeros because they are "trivial" solutions
[numer_success, numer_new_list] = try_remove(numer_list, digit)
[denom_success, denom_new_list] = try_remove(denom_list, digit)
if numer_success and denom_success:
# this means a digit was removed from the numerator AND the demoninator
if denom_new_list != [0]:
# make sure denominator isnt just a 0
if float(numer)/denom == float(list_as_number(numer_new_list))/list_as_number(denom_new_list):
numer_matches.append(numer_new_list[0])
denom_matches.append(denom_new_list[0])
numer = 1
denom = 1
for i in range(0,len(numer_matches)):
numer *= numer_matches[i]
denom *= denom_matches[i]
print "Value of denominator: ", Fraction(numer, denom).denominator
exit(0)