You have been tasked with assigning rooms to some mermaids who have visited the hotel. There are 9 mermaids:
- One is bald and bare-skinned
- One has a layer of fur
- One has a thick bark on their back
- One is covered in a coat of scales
- One is covered in a layer of slime
- One has thick, rough skin
- One has a bivalved shell
- One has a chitinous crust
- One is soft-bodied like a squid
There are only 3 rooms available, and due to past experiences you'd like to make sure at least one of them has no invertebrate mermaids (the shelled one, crusted one, or soft-bodied one), and that none of the rooms have 3 mermaids with a covering. You also think the exoskeletal mermaids (with the shell, crust, and bark) will appreciate being separate from each other.
The mermaids themselves have also told you some things. Specifically, they have informed you that the rough-skinned and the shelled mermaids need to be apart for the sake of their skin, and that the bare-skinned and furry mermaids have fallen out. Also, the slimy and soft-bodied mermaids would like to be together, as do the scaly and crust-having mermaids
Is there any way to sort out these mermaids' rooms?