def eighty_nine(m):
n = m
while n != 1 and n != 89 and n not in mem:
n = reduce(lambda accu, v: accu + to_digit(v) * to_digit(v), str(n), 0)
if m < 1000:
if n in mem:
mem[m] = mem[n]
else:
mem[m] = n == 89
return mem[m]
else:
return mem[n]
from strings import to_digit
s = ''
i = 1
while len(s) < 1000000:
s += str(i)
i += 1
print to_digit(s[0]) * to_digit(s[9]) * to_digit(s[99]) * to_digit(s[999]) * to_digit(s[9999]) * \
to_digit(s[99999]) * to_digit(s[999999])
from strings import to_digit, read_split
names = read_split('p022_names.txt')
names.sort()
s = 0
for i, n in enumerate(names):
score = reduce(lambda acc, x: acc + to_digit(x, '@'), n[1:-1], 0)
s += (i + 1) * score
print s
from strings import to_digit
from maths import factorial
m = 0
for n in xrange(3, 7 * factorial(9)):
s = 0
for c in str(n):
s += factorial(to_digit(c))
if s == n: m += s
print m
def facsum(n):
return reduce(lambda acc, v: acc + factorial(to_digit(v)), str(n), 0)
from strings import to_digit
ss = 0
for n in xrange(10, 6 * pow(9, 5)):
s = 0
for c in str(n):
s += pow(to_digit(c), 5)
if s == n: ss += s
print ss
def digits(n):
d = [0] * 10
s = str(n)
for c in s:
d[to_digit(c)] += 1
return d
from strings import to_digit, read_split
tri = []
for n in xrange(0, 20):
tri.append(n * (n + 1) / 2)
words = read_split('p042_words.txt')
tw = 0
for word in words:
s = 0
for w in word[1:-1]:
s += to_digit(w, '@')
for t in tri:
if s == t: tw += 1
print tw
from strings import to_digit
from maths import max
s = '7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450'
l = 13
m = 0
for i in xrange(0, len(s) - l):
v = 1
for j in xrange(i, i + l):
v *= to_digit(s[j])
m = max(m, v)
print m
