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.

Create a way to test for palindrom:



In [11]:

    
def is_palindrom(content):
    c=str(content)
    return c == c[::-1]

print(9009, is_palindrom(9009))
print(100, is_palindrom(100))









    



9009 True
100 False

Generate all products of numbers containing 3 digits and keep the max of this:



In [12]:

    
from itertools import combinations
max((i*j, i,j) for i,j in combinations(range(100, 1000),2) if is_palindrom(i*j) )









    Out[12]:





(906609, 913, 993)

and the smallest palindrom:



In [13]:

    
min((i*j, i,j) for i,j in combinations(range(100, 1000),2) if is_palindrom(i*j) )









    Out[13]:





(11211, 101, 111)

with number of palindroms



In [14]:

    
sum( 1 for i,j in combinations(range(100, 1000),2) if is_palindrom(i*j) )









    Out[14]:





1231

visualized



In [55]:

    
from itertools import permutations
all_pall = [(i*j, i,j) for i,j in permutations(range(100, 1000),2) if is_palindrom(i*j)]
s, x,y = zip(*all_pall)
import matplotlib
%matplotlib inline
matplotlib.pyplot.scatter(x,y,c=s)
matplotlib.pyplot.gray()
matplotlib.pyplot.show()

where are the palindroms



In [53]:

    
n, bins, patches = plt.hist(s, 200, facecolor='green', alpha=1)



In [ ]: