def euler036(limit):
''' The decimal number, 585 = 1001001001 (binary), is palindromic in both bases.
Find the sum of all numbers, less than one million, which are palindromic in base 10
and base 2.
(Please note that the palindromic number, in either base, may not include leading zeros.)
>>> euler036(1000000)
872187
'''
return sum(i for i in xrange(1, limit, 2) if all((palindrome(i), palindrome(stringbin(i)))))
def euler004(digits):
''' Largest palindrome product
A palindromic number reads the same both ways. The largest palindrome
made from the product of two 2-digit numbers is 9009 = 91 * 99.
Find the largest palindrome made from the product of two 3-digit numbers.
>>> euler004(2)
9009
>>> euler004(3)
906609
>>> euler004(4)
99000099
>>> euler004(5)
9966006699L
>>> euler004(6)
999000000999L
'''
for i in xrange(10 ** digits-1, 0, -1):
r = xrange(10 ** digits-1, i-1, -1)
try:
return max(j * k for j, k in
takewhile(lambda x: x[0] >= x[1], izip(r, reversed(r)))
if palindrome(str(j * k)))
except ValueError:
pass
def euler004a(digits):
''' Largest palindrome product
Brute force method.
>>> euler004a(2)
9009
>>> euler004(3)
906609
'''
return max(x*y for x in xrange(10 ** (digits-1), 10 ** digits)
for y in xrange(10 ** (digits-1), 10 ** digits)
if palindrome(str(x*y)))
