def curious(x, primes):
for i in range(1,8):
subnumber = euler_util.undigits(x[i:i+3])
q,r = divmod(subnumber, primes[i - 1])
if r != 0:
return False
return True
def run(target=8):
pgen = eu.GenFinder(eu.gen_primes())
# Loop over all prime numbers
for prime_idx in eu.numbers():
curr_prime = pgen[prime_idx]
curr_digits = eu.digits(curr_prime) # digits in current prime
# Get all selections of indices from current digits
for rindices in eu.selections(range(len(curr_digits))):
rzero = 0 in rindices
if len(rindices) == 0:
continue
found_primes = []
work_digs = curr_digits[:] # copy digits of current prime
# Choose the digit which we will insert at each index in rindices (the current selection)
for replacement in range(10):
if replacement == 0 and rzero:
continue
for rindex in rindices:
work_digs[rindex] = replacement
prime_idx = pgen.find(eu.undigits(work_digs))
if prime_idx != -1:
found_primes.append(pgen[prime_idx])
if len(found_primes) >= target:
# print "answer =",min(found_primes),found_primes,rindices
return min(found_primes)
def is_lychrel(x):
digs = eu.digits(x)
for i in range(49):
rdigs = digs[:]
rdigs.reverse()
x += eu.undigits(rdigs)
digs = eu.digits(x)
if eu.palindrome(digs):
return False
return True
def run():
primes = [p for p in euler_util.primes(17)]
sum = 0
for c in euler_util.combos(range(10)):
if c[0] == 0:
continue
if curious(c, primes):
# print c
sum += euler_util.undigits(c)
def run():
primes = [p for p in euler_util.primes(int(math.ceil(math.sqrt(987654321))))]
max = 0
toks = []
for i in [1,2,3,4,5,6,7,8,9]:
toks.append(i)
for c in euler_util.combos(toks):
x = euler_util.undigits(c)
if is_prime(x, primes) and x > max:
max = x
def run():
data = {}
for i in range(1, 10000):
val = pow(i,3)
nval = eu.digits(val)
nval.sort()
nval.reverse()
nval = eu.undigits(nval)
try:
data[nval].append(val)
except KeyError:
data[nval] = [val]
min = None
for k,v in data.items():
if len(v) == 5:
if min is None or v[0] < min:
min = v[0]
return min
import euler_util
def complete(x):
y = x[:]
y.sort()
return y == range(1, 10)
max_val = 0
for digits in euler_util.permutations(range(1,10), 4):
base_value = euler_util.undigits(digits)
for i in euler_util.numbers(2):
curr_value = base_value * i
digits += euler_util.digits(curr_value)
if len(digits) > 9:
break
elif len(digits) == 9:
if complete(digits):
val = euler_util.undigits(digits)
# print base_value,i,val
if val > max_val:
max_val = val
break
# print max_val