# Who stole whose hat and coat?

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

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.

• That's good to hear. I was mainly just checking to see if other people would get the same answer as me :) Thanks! Nov 8, 2018 at 20:23