On a table lies a 13 x 14 board with black and white tiles, of which we can alter the colours with 27 levers. With each of the levers we can swap the colour of each row or column, so any black tiles in this row (or column respectively) turn white and vice versa. We can use the levers infinite number of times. Starting from all 182 tiles in their black position, how many different layouts can we achieve?
It would be easy to say that if for each tile we have have two values, black and white, it would be $2^{27}$ but I don't think so...