def check(n, d):
nl = digits.get_all(n)
dl = digits.get_all(d)
for i in xrange(2):
for j in xrange(2):
if nl[1-i] == dl[1-j] and 1.0 * n / nl[i] == 1.0 * d / dl[j]:
print "%s/%s -> %s/%s" % (n, d, nl[i], dl[j])
return True
def digit_at(place):
index_into_power = place
power = 1
while index_into_power > get_digits_in_power(power):
index_into_power -= get_digits_in_power(power)
power += 1
index_into_power -= 1
number_in_power = index_into_power / power
digit_in_number = index_into_power % power
number = (10 ** (power-1)) + number_in_power
digit = digits.get_all(number)[digit_in_number]
return digit
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
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))
pprint(answers)
print sum(set(eq[2] for eq in answers))
"""
The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.
There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.
How many circular primes are there below one million?
"""
import digits
import primes
from itertools import permutations
pbm = filter(lambda p : 0 not in digits.get_all(p), primes.get_primes(1000000))
pbm = filter(lambda p : 2 not in digits.get_all(p), pbm)
pbm = filter(lambda p : 4 not in digits.get_all(p), pbm)
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:
"""
It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order.
Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits.
"""
import digits
from math import log
i = 1
while True:
if int(log(6*i, 10)) == int(log(i, 10)):
c = set(digits.get_all(i))
nope = False
for n in xrange(2, 7):
if c != set(digits.get_all(i*n)):
nope = True
break
if not nope:
print i
exit(0)
i += 1
"""
145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.
Find the sum of all numbers which are equal to the sum of the factorial of their digits.
Note: as 1! = 1 and 2! = 2 are not sums they are not included.
"""
import digits
from math import factorial
from pprint import pprint, pformat
ans = 0
for i in xrange(1, 2000000):
if sum([factorial(n) for n in digits.get_all(i)]) == i:
ans += i
print i
"""
The decimal number, 585 = 10010010012 (binary), is palindromic in both bases.
Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.
(Please note that the palindromic number, in either base, may not include leading zeros.)
"""
import digits
ans = 0
for i in xrange(1, 1000000):
dl = digits.get_all(i)
dlr = (dl * 1)
dlr.reverse()
bl = digits.get_all(i, 2)
blr = (bl * 1)
blr.reverse()
if dl == dlr and bl == blr:
print i
ans += i
print ans
def unique_digits(n):
dgs = digits.get_all(n)
return len(set(dgs)) == len(dgs)
first_six_primes = primes.primes[:6]
first_six_primes.reverse()
multiples_of_17 = [n for n in xrange(99, 1000) if divides(17, n) and unique_digits(n)]
alldigits = set(xrange(10))
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
sum = 0
for multiple in multiples_of_17:
number_so_far = digits.get_all(multiple)
sum += sum_interestings(number_so_far, first_six_primes)
print sum
