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.

I'll assume a cane is also considered an article of clothing...

Just draw a grid of which things each took home, with the four people on one axis and the 'clothing' on the other. Fill each blank with an A, B, C, or D to represent the rightful owner of that particular item, and each letter can appear only once in each row or column.

Here's what we are given:

      A B C D


coat| A B · ·


hat | · · C ·


glvs| · · · D


cane| C · · ·

We are told what correct article each person has, and that A does not have C's cane.

A cannot have his own cane, since he has his own coat, and we are told that he does not have C's cane. Therefore, he has B's cane or D's cane.

If he has B's cane, he must have D's hat and C's gloves. Then, however, B must have A's hat (D and C's hats are taken, and B already has his own coat). Then, B has one article from A and of his own, but C and D's gloves are already taken, so that cannot work.

      A B C D


coat| A B · ·


hat | D A C ·


glvs| C ? · D


cane| B · · ·

Nothing can go in the ? spot without a contradiction.

Therefore, A must have D's cane. He must also, then, have C's gloves (C has his own hat already) and B's hat.

      A B C D


coat| A B · ·


hat | B · C ·


glvs| C · · D


cane| D · · ·

Now, look at what B has.

B must have C's cane, A's gloves, and D's hat (the other articles for each person are already all taken.

      A B C D


coat| A B · ·


hat | B D C ·


glvs| C A · D


cane| D C · ·

All the pairs of gloves are taken but one..

C must have B's gloves, the only ones left. He also took A's cane (D's is gone by now), and D's coat.

      A B C D


coat| A B D ·


hat | B D C ·


glvs| C A B D


cane| D C A ·

Finally, by elimination, D has C's coat, A's hat, and B's cane.

      A B C D


coat| A B D C


hat | B D C A


glvs| C A B D


cane| D C A B

Posted by DJ on 2003-09-02 18:34:26