#4 - Largest palindrome product

23 Jul 2015 in Project Euler on 5%, Brute force

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 x 99.

Find the largest palindrome made from the product of two 3-digit numbers.

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First, we need a function to determine if a number is a palindrome. Using Python, we can convert the number to a string, reverse it, and check if they are equal.

# file: "problem004.py"
def isPalindrome(n):  
   num = str(n)  
   return num == num[::-1]

Next, the built-in method itertools.combinations allows to quickly iterate through all products of two 3-digit numbers. Because we want the largest, we will reverse the list of products after removing duplicates, and select the first palindrome we find.

# file: "problem004.py"
numbers = sorted(set([a * b for a, b in combinations(range(100, 1000), r=2)]))  
  
i = -1  
while not isPalindrome(numbers[i]):  
   i -= 1  
  
print(numbers[i])

Running this short code gives us

906609
0.07893140008673072 seconds.

Therefore, 906609 is our answer.