InterviewBit Problems   Genie and Hats : Unsolved

About the Genie and Hats : Unsolved category (1)
If they are perfect logicians, they should be able to solve in 1 day (2)
Is there no communication between the residents? (1)
Why is the answer not 1 day? (1)
Is 1 day also answer (2)
Is it planned beforehand? (2)
Please give me some clarfication of the question (2)