Four gentlemen (A, B, C, and D) went to an expensive restaurant to dine. They checked their coats, hats, gloves, and canes at the door (each of the gentlemen had one of each). But when they checked out, there was a mix up, and each of the men ended up with exactly one article of clothing (a pair of gloves is considered a single article of clothing) belonging to each one of the four.

A and B ended up with their own coats, C ended up with his own hat, and D ended up with his own gloves. A did not end up with C's cane.

State whose coat, hat, gloves, and cane each of the gentlemen ended up with.

Two gentlemen have their own coat. That leaves two coats to distribute among the other two men. Since each man has one and only one item of his own, C and D cannot each have their own coat--they have received another item of their own (hat and gloves, respectively). Hence, C has D's coat and D has C's coat.

Each man must have one item each from the other four gentlemen. We have already assigned a couple items to C and D. C cannot have his own cane, nor D's cane; likewise, D cannot have either C or D's cane. C and D together have the canes belonging to A and B. Therefore, A and B together must have the canes belonging to C and D. Since A does not have C's cane (as stated in the problem description), A must have D's cane; B has C's cane.

Now that we have assigned a couple items to A and B, we can try to figure out whose hats and gloves they have. A has one of his own items, plus one of D's. Meanwhile, C's hat has already been placed. Therefore, A must have B's hat. Now with one item from A, B, and D, we know that A must have C's gloves.

Likewise, we have already figured out a couple of the items that B walked out of the restaurant with. He has one of his own items (coat) plus one from C (cane); the other two items must come from A and D. D's gloves have been assigned already; B must have A's gloves, and his final item (hat) comes from D.

We have now placed three of the hats: C has his own, while A has B's hat and B has D's hat. The last hat (A's) goes to D. Likewise, we have placed three of the gloves. C must have the remaining pair of gloves from B.

The last two items are A's and B's canes. Each gentleman has one item from each of the others; we've already placed C with items from B, C, and D. C must have A's cane. Finally, D must have B's cane.

A: A's coat, B's hat, C's gloves, D's cane
B: B D A C
C: D C B A
D: C A D B

Posted by Andrew on 2003-09-24 13:48:39