problem00038.py

#!/usr/bin/env python

# Pandigital multiples

# Problem 38
# Take the number 192 and multiply it by each of 1, 2, and 3:

    # 192 × 1 = 192
    # 192 × 2 = 384
    # 192 × 3 = 576
# By concatenating each product we get the 1 to 9 pandigital, 192384576. We will call 192384576 the concatenated product of 192 and (1,2,3)

# The same can be achieved by starting with 9 and multiplying by 1, 2, 3, 4, and 5, giving the pandigital, 918273645, which is the concatenated product of 9 and (1,2,3,4,5).

# What is the largest 1 to 9 pandigital 9-digit number that can be formed as the concatenated product of an integer with (1,2, ... , n) where n > 1?

def concatenatedproduct(n, nums):
    return ''.join(map(lambda x: str(n * x), nums))

def ispandigital(x, n=9):
    return ''.join(sorted(str(x))) == '123456789'


xs = (concatenatedproduct(j, range(1, k + 1)) for j in range(1, 10000) for k in range(2, 10))
print(max(x for x in xs if ispandigital(x)))