def muls(n):
d = set([0])
dig = []
for mul in count(1):
t = to_digits(mul * n)
if len(t) != len(set(t)):
return False
if set(t) & d:
return False
else:
d |= set(t)
dig += t
if len(d) == 10:
return dig
elif len(d) > 10:
raise Exception
#!/usr/bin/env python
from itertools import count
from common import to_digits
powers = [n**5 for n in range(0, 10)]
t = 0
for a in count(10):
if a > 1000000:
break
s = sum([powers[d] for d in to_digits(a)])
if a == s:
t += a
print(t)
#!/usr/bin/env python
from common import to_digits
MAX = 9
def is_n_pandigital(digits, end=MAX):
ds = sorted(range(1, end + 1))
di = sorted(digits)
return ds == di
found = set()
for m1 in range(1, 10000):
for m2 in range(1, 10000):
mult = m1 * m2
if mult > 98765:
# Naive way of making it faster
break
digits = to_digits(m1) + to_digits(m2) + to_digits(mult)
if is_n_pandigital(digits):
found.add(mult)
print(sum(found))
#!/usr/bin/env python
from common import factorial, to_digits
from itertools import count
fs = list(factorial(n) for n in range(0, 10))
S = 0
for i in count(10):
if i > 100000:
break
s = sum(fs[d] for d in to_digits(i))
if s == i:
S += i
print(S)
#!/usr/bin/env python
from common import is_prime, to_digits
for n1 in range(1000, 10000 - (3330 * 2)):
n2 = n1 + 3330
n3 = n2 + 3330
d1 = to_digits(n1)
d2 = to_digits(n2)
d3 = to_digits(n3)
if not (sorted(d1) == sorted(d2)):
continue
if not (sorted(d1) == sorted(d3)):
continue
if not is_prime(n1):
continue
if not is_prime(n2):
continue
if not is_prime(n3):
continue
s = sum([a * 10**k for k, a in enumerate(reversed(d1 + d2 + d3))])
print(s)
from common import to_digits
from fractions import Fraction
def remove_digit(d, l):
if l[0] == d:
return l[1]
else:
return l[0]
nprod = 1
dprod = 1
for d in range(11, 100):
for n in range(10, d):
dd = to_digits(d)
dn = to_digits(n)
common = set(dd) & set(dn)
if len(common) != 1:
# We don't want empty sets or bigger than one (to avoid /0)
continue
digit = common.pop()
if not digit:
# Remove trivial examples
continue
n2 = remove_digit(digit, dn)
d2 = remove_digit(digit, dd)
def dig(n):
return sorted(to_digits(n))