Brute force

The brute force approach for this problem is very simple, as the task of identifying numbers sharing the same digit has already been solved in the Prime permutations problem with the Brute force approach.

The remaining step consist of iterating through all positive numbers until all products wth number from 2 to 6 are permutations of the original integer.

From solution1.py:

def permuted_multiples():
    for i in itertools.count(1):
        if all(sorted(str(i)) == sorted(str(i * j)) for j in range(2, 7)):
            return i