Day 1: largest palindrome

Question 1)

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.

Answer:

The largest palindrome can be written as: abccba Which then simpifies to: 100000a + 10000b + 1000c + 100c + 10b + a And then: 100001a + 10010b + 1100c Factoring out 11, you get: 11(9091a + 910b + 100c) So the palindrome must be divisible by 11. Seeing as 11 is prime, at least one of the numbers must be divisible by 11.

#Create a sequence from 100 to 999

three_dig = range(100,1000)
# and an empty list for the palindromes

list_palindromes = []
# loop twice over the number sequence

for n1 in three_dig:    

for n2 in three_dig:       

 # Get the product       

 number =  n1 * n2
 # Transform it in string      

 number = str(number)
 # Check the whole string to test      

  # if it's a palindrome       

 if number == number[::-1]:         

   # Add the palindrome to the list        

 list_palindromes.append(int(number))

print max(list_palindromes)