def problem36():
""" Double-base palindromes
Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.
"""
return sum(x for x in range(1, 1000000) if
mathhelper.is_palindromic(x) and mathhelper.is_palindromic(int(bin(x)[2:])))
def test_is_palindromic(self):
self.assertEqual(mathhelper.is_palindromic(-1), True)
self.assertEqual(mathhelper.is_palindromic(0), True)
self.assertEqual(mathhelper.is_palindromic(1), True)
self.assertEqual(mathhelper.is_palindromic(11), True)
self.assertEqual(mathhelper.is_palindromic(13), False)
self.assertEqual(mathhelper.is_palindromic(131), True)
self.assertEqual(mathhelper.is_palindromic(199991), True)
self.assertEqual(mathhelper.is_palindromic(1999991), True)
self.assertEqual(mathhelper.is_palindromic(234667556), False)
def problem4():
""" 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.
"""
return max(
x * y for (x, y) in itertools.product(range(100, 1000), repeat=2) if
mathhelper.is_palindromic(x * y))
