Problem 38 : Pandigital multiples

Problem Statement

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?

Solution

largest = 0
for i in range(1,10000):
	
	multiplication = ''
	
	integer = 1
	
	while len(multiplication) < 9:
		
		multiplication += str(i*integer)
		
		integer += 1
		
	if ((len(multiplication) == 9) and (len(set(multiplication)) == 9) 
		and ('0' not in multiplication)):
	
		if int(multiplication) > largest:
			largest = int(multiplication)

print (largest)

Output

932718654