shieldsd

from math import sqrt
from itertools import count
from itertools import islice

def f(n): return n * (3 * n - 1) / 2                  # nth pentagonal
def p(n): return not ((sqrt(24 * n + 1) + 1) / 6) % 1 # is  pentagonal

print islice((abs(f(i) - f(j))
                for i in count(2)
                    for j in xrange(i - 1, 1, -1)

shieldsd

def comb(l):
    if len(l) == 0:
        yield []
    else:
        for i in range(len(l)):
            for cc in comb(l[:i] + l[i + 1:]):
                yield [l[i]] + cc
def combn(n):
    l = [c for c in str(n)]
    return [int(''.join(x)) for x in comb(l)]

shieldsd

from math import sqrt

def istriangle(n):
    return (sqrt(8 * n + 1) - 1) / 2 % 1 == 0

words = open('words.txt').readline().replace('"', '').split(',')

print sum(1 for _ in (filter(lambda x: istriangle(x),
            (sum(ord(c) - ord('A') + 1 for c in w)
                for w in words))))

shieldsd

from itertools import chain
from math import sqrt

def comb(l):
    if len(l) == 0:
        yield []
    else:
        for i in range(len(l)):
            for cc in comb(l[:i] + l[i + 1:]):
                yield [l[i]] + cc

shieldsd

from operator import mul
from itertools import takewhile

def nth():
    i = 1
    s = '1'
    while 1:
        yield i, s[i - 1]
        i += 1
        s += str(i)

shieldsd

def perimeters(n):
    s = 0
    for a in range(1, n / 3):
        if n * (n - 2 * a) % (2 * (n - a)) == 0:
            s += 1
    return s

print max((perimeters(i), i) for i in range(2, 1000, 2))[1]

shieldsd

def pandigital(s):
    return ''.join(sorted(s)) == '123456789'

print max(filter(pandigital, (str(n) + str(n * 2)
                    for n in range(9876, 9123, -1))))

shieldsd

from itertools import count
from itertools import islice
from math import sqrt

def truncated(n):
    l, s = [], 10
    while n / s > 0:
        l.extend([n / s, n % s])
        s *= 10
    return set(l)

shieldsd

def palindrome(s):
    return s == s[::-1]

def d2b(n):
    s = ''
    while n:
        if n & 1:
            s = '1' + s
        else:
            s = '0' + s

shieldsd

from itertools import takewhile
from itertools import count
from math import sqrt
from math import log

def rotate(n):
    d = int(log(n, 10))
    m = 10 ** d
    for _ in range(d):
        r = n % 10