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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 dont 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 dont know will always be: I have a black hut
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