challenge3.py

import itertools


def count_inversions(my_list):
    iterations = 0
    for elem in my_list:
        if elem != 0:
            for number in my_list[:my_list.index(elem)]:
                if number > elem:
                    iterations += 1
    return iterations


def to_tuple(board, size):
    new_list = [tuple(board[i:i+size]) for i in range(0, len(board), size)]
    return tuple(new_list)


def solvable(board, size):
    inversions = count_inversions(board)
    if size % 2 == 1 and inversions % 2 == 0:
        return True
    if size % 2 == 0 and ((blank_elem_index(board, size) % 2 == 0) == (inversions % 2 == 0)):
        return True
    return False


def blank_elem_index(board, size):
    my_tuple = to_tuple(board, size)
    for elem in my_tuple:
        if 0 in elem:
            return my_tuple.index(elem) + 1


def solvable_tiles(size=4):
    board = [number for number in range((size) ** 2)]
    for perm in itertools.permutations(board):
        inversions = count_inversions(perm)
        if solvable(board, size):
            yield to_tuple(perm, size)
        else:
            yield


if __name__ == '__main__':
    my = solvable_tiles(4)
    print(next(my))
    print(next(my))
    print(next(my))
    print(next(my))
    print(next(my))