def test_ispalindrome(self):
self.assertEqual(euler.ispalindrome(1), True)
self.assertEqual(euler.ispalindrome(11), True)
self.assertEqual(euler.ispalindrome(12), False)
self.assertEqual(euler.ispalindrome(111), True)
self.assertEqual(euler.ispalindrome(123), False)
self.assertEqual(euler.ispalindrome(1221), True)
self.assertEqual(euler.ispalindrome(1231), False)
def biggestPal():
i = 100 # Smallest 3 digit number
j = 100 # Largest 3 digit number
maxp = 0
# all products of 3 digit numbers
while i < 1000:
while j < 1000:
n = i * j
if euler.ispalindrome(n):
maxp = max(maxp, n)
j += 1
i += 1
j = 0
return maxp
"""
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.)
"""
from euler import ispalindrome
sum = 0
for n in range(1,1000000):
if ispalindrome(str(n)) and ispalindrome( bin(n)[2:].lstrip('0')):
# print "Palindrome: " + str(n) + " --bin-- " + bin(n)
sum += n
print sum
import math
import euler
N = 10 ** 8
sums = []
for i in xrange(1, int(math.sqrt(N))):
for j in xrange(i + 1, int(math.sqrt(N)) + 1):
s = sum([x ** 2 for x in xrange(i, j + 1)])
if s >= N:
break
if euler.ispalindrome(s):
sums.append(s)
print sum(set(sums))
def test_ispalindromeSingleDigit(self):
self.assertTrue(ispalindrome(0))
self.assertTrue(ispalindrome(1))
self.assertTrue(ispalindrome(2))
self.assertTrue(ispalindrome(3))
self.assertTrue(ispalindrome(4))
self.assertTrue(ispalindrome(5))
self.assertTrue(ispalindrome(6))
self.assertTrue(ispalindrome(7))
self.assertTrue(ispalindrome(8))
self.assertTrue(ispalindrome(9))
self.assertFalse(ispalindrome(10))
self.assertFalse(ispalindrome('01101'))
self.assertFalse(ispalindrome('1110'))
self.assertTrue(ispalindrome('31313'))
self.assertTrue(ispalindrome('0110'))
self.assertTrue(ispalindrome('010'))
self.assertTrue(ispalindrome('11'))
self.assertTrue(ispalindrome('121'))
import collections
import math
import euler
# Trial and error until we find the 5 numbers.
N = 10 ** 9
I = int(round(math.sqrt(N)))
J = int(round(N ** (1 / 3.0)))
S = collections.defaultdict(list)
# Generate all combinations of i^2 + j^3 <= N.
# Save away all the palindromes.
for i in range(2, I + 1):
for j in range(2, J + 1):
n = i ** 2 + j ** 3
if euler.ispalindrome(n):
S[n].append((i, j))
palindromes = []
for key in S.keys():
if len(S[key]) == 4:
palindromes.append(key)
assert len(palindromes) == 5
print sum(palindromes)
#!/bin/env
import euler
largest_palindrome = 0
for i in range(100, 1000):
for j in range(100, 1000):
product = i * j
if product > largest_palindrome and euler.ispalindrome(product):
largest_palindrome = product
print largest_palindrome
