E004
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.

水仙花数是从左向右和从右向左读都相同的自然数。求两个三位数的乘积中最大的水仙花数。

def problem4():
    min, max = 100, 999
    def isPalindromic(num):
        if num<=10:
            return False
        digits = list(str(num))
        revdigs = list(str(num))
        revdigs.reverse()
        return digits==revdigs

    x = y = avg = max
    while avg>=min:
        num = x*y
        if isPalindromic(num):
            return x,y,num
        elif x<=min or y>=max:
            avg -= 0.5
            x = int(avg)
            y = int(avg+0.5)
        else:
            x -= 1
            y += 1


if __name__=='__main__':
    print str(problem4())

考虑两个三位数乘积最大的是 999x999, (平均数999)
其次是 998x999,           (平均数998.5)
再次是 998x998, 997x999,  (平均数998)
然后是 997x998, 996x999,  (平均数997.5)
       ......