# 932718654
import euler
N = 9
m = 0
for a in xrange(1, 10 ** (N/2)):
n = 0
s = ''
while len(s) < N:
n += 1
s += str(a * n)
if len(s) == N and euler.digit_usage(int(s)) == int('1' * 9 + '0', 2):
if int(s) > m:
m = int(s)
print m
# 100
import math
import euler
D = 2
N = 10 ** D
np = 1
dp = 1
for n in xrange(N/10, N):
for d in xrange(n+1, N):
nn = euler.digit_usage(n)
dd = euler.digit_usage(d)
c = nn & dd
if c == 0 or c == 1 or math.log(c, 2) % 1.0 != 0 or \
nn ^ c == 0 or dd ^ c == 0:
continue
n2 = math.log(nn ^ c, 2)
d2 = math.log(dd ^ c, 2)
if d2 != 0 and float(n) / d == n2 / d2:
np *= n
dp *= d
np, dp = euler.reduce_fraction(np, dp)
print dp
# 45228
import euler
p = {}
for a in xrange(1, 10000):
for b in xrange(a+1, 10000 / a + 1):
c = a * b
aa = euler.digit_usage(a)
bb = euler.digit_usage(b)
cc = euler.digit_usage(c)
if aa & bb & cc == 0 and aa | bb | cc == int('1111111110', 2):
p[c] = True
print sum(p.keys())
# 142857
import euler
N = 6
d = 1
while True:
for n in range(10 ** d, 2 * 10 ** d):
found = True
nn = euler.digit_usage(n)
for i in range(2, N + 1):
if nn != euler.digit_usage(n * i):
found = False
break
if found:
print n
break
if found:
break
d += 1
# 296962999629
import euler
D = 4
N = 10 ** D
S = 3330
sieve = euler.prime_sieve(N)
for a in xrange(N/10+1, N, 2):
b = a + S
c = b + S
if a != 1487 and sieve[a] and sieve[b] and sieve[c]:
aa = euler.digit_usage(a)
if aa == euler.digit_usage(b) and aa == euler.digit_usage(c):
print '%d%d%d' % (a, b, c)
break
# 16695334890
import math
import euler
s = 0
for a in xrange(1, 999/17):
aa = euler.digit_usage(a * 17, 3)
for b in xrange(1, 999/13):
if (a * 17) / 10 != (b * 13) % 100:
continue
for c in xrange(1, 999/11):
if (b * 13) / 10 != (c * 11) % 100:
continue
for d in xrange(1, 999/7):
if (c * 11) / 10 != (d * 7) % 100:
continue
dd = euler.digit_usage(d * 7, 3)
if aa & dd != 0:
continue
for e in xrange(1, 999/5):
if (d * 7) / 10 != (e * 5) % 100:
continue
for f in xrange(1, 999/3):
if (e * 5) / 10 != (f * 3) % 100:
continue
for g in xrange(999/2):
if (f * 3) / 10 != (g * 2) % 100:
continue
gg = euler.digit_usage(g * 2, 3)
if aa & gg != 0 or dd & gg != 0:
continue