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After a Halloween party with four guests:

  1. All guests took a coat and a hat of another guest (i.e., every one took a coat and a hat but not their own).
  2. No guest took a coat and a hat from the same person.
  3. A took the coat of the person whose hat B took.
  4. B’s coat was taken by the same person who took the hat of A.
  5. C took D’s hat.

My solution:

  • A took B's hat and C's coat
  • B took C's hat and D's coat
  • C took D's hat and A's coat
  • D took A's hat and B's coat

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    Your solution is the ONLY solution because:

    First of all, we know C took D's hat.

    Now, let's look at clue 4. C took D's hat, so A couldn't have taken D's coat (because then B would have had to take D's hat, which is impossible because C took it).

    Next it's possible to determine D took A's hat and B's coat because A and B can't take their own hat or coat, and C took D's hat.

    B had to have taken D's coat, because A can't and C's taken D's hat.

    From there, it's possible to deduce the rest easily.

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    • $\begingroup$ That's good to hear. I was mainly just checking to see if other people would get the same answer as me :) Thanks! $\endgroup$ – GodOfMaths Nov 8 '18 at 20:23

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