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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?

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    $\begingroup$ I feel like this is missing the number of rooms we have. Otherwise it seems pretty trivial to put every mermaid in their own room except the two pairs at the end who can share. I also don't think there's really a good way to reason about which mermaids are invertebrates, that information is probably necessary for that restriction to be doable. $\endgroup$ Nov 25 at 20:00
  • $\begingroup$ @GoblinGuide Do my edits help? $\endgroup$ Nov 25 at 20:03
  • $\begingroup$ "none of the rooms have 3 mermaids with a covering" - what exactly counts as a covering? Fur, bark, scales, slime, shell, crust? So only bare-skinned, rough-skinned, and soft-bodied don't have a covering? $\endgroup$ Nov 25 at 21:35
  • $\begingroup$ @Randal'Thor Yes, that's exactly right $\endgroup$ Nov 25 at 22:05
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We have seven criteria to satisfy:

  1. At least one room has none of Shelled, Crusted, Soft-bodied.
  2. None of the rooms have 3 of Furry, Bark, Scaly, Slimy, Shelled, Crusted together.
  3. Shelled, Crusted, and Bark should all be in different rooms.
  4. Rough-skinned and Shelled can't be together.
  5. Bare-skinned and Furry mermaids can't be together.
  6. Slimy and Soft-bodied should be together.
  7. Scaly and Crusted should be together.

Let's start from criterion 3 and say that

Shelled is in room $1$, Crusted is in room $2$, Bark is in room $3$.

From criteria 1 and 7,

Soft-bodied is not in room $3$ and Scaly is in room $2$.

From criterion 6,

Slimy and Soft-bodied are together, not in room $3$ by above, not in room $2$ since that would violate criterion 2, therefore in room $1$ with Shelled.

Now we have

Shelled, Slimy, Soft-bodied in room $1$, Crusted and Scaly in room $2$, Bark in room $3$. The only ones still to place are Furry, Bare-skinned, Rough-skinned. Also, criteria 1 and 3 and 6 and 7 are now satisfied, so we just have to make sure of criteria 2 and 4 and 5.

By criteria 4 and 2,

Rough-skinned isn't in room $1$ and Furry isn't in room $2$.

It is possible to satisfy all conditions by putting

Bare-skinned in room $2$ and Rough-skinned and Furry in room $3$.

So the answer is yes.

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