bob = set()

for i in range(4):
    for j in range(4):
        bob.add((i,j))

print len(bob)


def get_potential_additions(element_list, parent_list):

    if len(element_list) == 0:
        return parent_list

    x_vals = [item[0] for item in element_list]
    y_vals = [item[1] for item in element_list]

    potential_adds = filter(lambda item: (item[0] not in x_vals and item[1] not in y_vals), parent_list)

    return potential_adds


def get_all_mappings(operating_set, current_list = [], all_groups = []):

    additions = get_potential_additions(current_list, operating_set)
    #print additions

    if len(additions) == 0:
        all_groups.append(tuple(sorted(current_list)))

    for element in additions:
        current_list_copy = list(current_list)
        current_list_copy.append(element)
        get_all_mappings(additions, current_list_copy, all_groups)

    return set(all_groups)


get_all_mappings(list(bob))