We can state the problem without telling, what the rear and the middle captive said, instead, we can simply ask for analysis – which is:

If the bottom guy has a black hut he will know it from the two “I don’t know” answers. If he has a white hut, he will learn about it from either the top captive – (B – W – W) or the middle one – (X – B – W).

Interestingly enough, the first answer other than “I don’t know” will always be: “I have a black hut”