def luhn_checksum(string):
    """
    Compute the Luhn checksum for the provided string
    (representing numbers).
    """
    digits = list(map(int, string))
    odd_sum = sum(digits[-1::-2])
    even_sum = sum([sum(divmod(2 * d, 10)) for d in digits[-2::-2]])
    return (odd_sum + even_sum) % 10