def sum_interestings(number_so_far, primes):
numbers_unused = alldigits - set(number_so_far)
if len(numbers_unused) == 1:
if 0 in numbers_unused:
return 0
return digits.collapse(list(numbers_unused) + number_so_far)
test = number_so_far * 1
sum = 0
for number in numbers_unused:
test = [number] + number_so_far
if divides(primes[0], digits.collapse(test[:3])):
sum += sum_interestings(test, primes[1:])
return sum
def test_guess(guess, best):
# print "Trying ", guess
multiplier = 0
list = []
while True:
multiplier += 1
list += digits.get_all(guess * multiplier)
# print " list after multiplying by %s" % multiplier, list
if 0 in list:
# print " No zeroes allowed!"
break
if digits.collapse(list) < best / (10 ** (9 - len(list))):
# print " %s < %s, giving up on %s" % (digits.collapse(list), best / (10 ** (9 - len(list))), guess)
break
if len(set(list)) < len(list):
# print " list contains duplications, giving up"
break
if len(list) == 9:
# print "***** found a contender! %s results in %s" % (guess, digits.collapse(list))
return digits.collapse(list)
return -1
l = len(dgs)
done = False
ans = 0
while not done:
i = l - 1
dgs[i] += 1
while dgs[i] > 9:
dgs[i] = 0
i -= 1
if i < 0:
done = True
break
dgs[i] += 1
for i in xrange(1, l):
if dgs[i] < dgs[i - 1]:
dgs[i] = dgs[i - 1]
spd = digits.get_all(sum_of_powers(dgs, 5))
n = digits.collapse(spd)
spd.sort()
if digits.collapse(dgs) == digits.collapse(spd):
ans += n
print n
print ans
assert sum_of_powers(digits.get_all(1634), 4) == 1634
assert sum_of_powers(digits.get_all(8208), 4) == 8208
assert sum_of_powers(digits.get_all(9474), 4) == 9474
i -= 1
if i < 0:
raise StopIteration
l[i] += 1
for i in xrange(1, length):
if l[i] > 10 - length + i:
l[i] = l[i-1] + 1
yield l * 1
answers = set([])
unique_ascending_lists = lister(4)
for unique_ascending_list in unique_ascending_lists:
unique_lists = permutations(unique_ascending_list)
for unique_list in unique_lists:
number = digits.collapse(unique_list)
ps = set(unique_list)
# print "number: %s" % number
factors = primes.factor(number)
# print "factors: %s" % factors
factorpairs = divisions(factors)
# print unique_list
for pair in factorpairs:
# print " %s" % (pair,)
multiplicand = functools.reduce(operator.mul, pair[0], 1)
m1s = set(digits.get_all(multiplicand))
multiplier = functools.reduce(operator.mul, pair[1], 1)
m2s = set(digits.get_all(multiplier))
if len(m1s) + len(m2s) == 5 and m1s | m2s | ps == set([1,2,3,4,5,6,7,8,9]):
answers.add((multiplicand, multiplier, number))
"""
We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.
What is the largest n-digit pandigital prime that exists?
"""
import primes
import digits
from itertools import permutations
for i in xrange(9, 0, -1):
for p in permutations(xrange(i, 0, -1)):
potential = digits.collapse(p)
if primes.is_prime_greedy(potential):
print potential
exit(0)
pbm = filter(lambda p : 5 not in digits.get_all(p), pbm)
pbm = filter(lambda p : 6 not in digits.get_all(p), pbm)
pbm = filter(lambda p : 8 not in digits.get_all(p), pbm)
cpms = set([2, 5])
ncpms = set([])
def rotations(l):
l2 = l * 1
for i in xrange(len(l2)):
l2 = l2[1:] + [l2[0]]
yield l2
for prime in pbm:
if prime not in cpms and prime not in ncpms:
perms = []
circular = True
for ppml in rotations(digits.get_all(prime)):
ppm = digits.collapse(ppml)
if not ppm in pbm:
circular = False
break
perms.append(ppm)
if circular:
# print perms
cpms |= set(perms)
else:
ncpms |= set(perms)
#print cpms
print len(cpms)
def get_family(guess):
candidates = [digits.collapse([(d if d < 10 else nd) for d in guess]) for nd in xrange(10)]
return [candidate for candidate in candidates if primes.is_prime(candidate)]