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.
(In reply to
Solution (spoiler) by SilverKnight)
For those who want a hint on how to solve it... It's possibly easiest if you set up a 4x4 grid (such as ABCD along the side of the grid, and "coat", "hat", "glove", and "cane" along the top).
Then, fill in the LETTER of the person's item that each person took. So... based on the "given" rules that the problem stated. Write in A in {A, coat}, B in {B, coat}, C in {C, hat}, and D in {D, gloves}
Next, note that C and D each already have one of their own items, therefore neither has their own Coat. The only remaining solution (for coats) is that C has D's coat, and D has C's coat, so... fill in D for {C, coat} and C for {D, coat}.
Next, note that this means that the two remaining "holes" in C's row must be filled by 'A' & 'B'. Similarly, the remaining "holes in D's row must also be filled by 'A' & 'B'. Both rows include the CANE column. Okay, so this means that C has A or B's cane, D has A or B's cane, and the GIVEN rules imply that A has A, B, or D's cane. Since, if A has EITHER A or B's cane, then only the OTHER is free for C and D, we have an impossibility. Therefore, A has D's cane--fill in D for {A, cane}. Also, since A and B's canes are taken by C and D, B must have C's cane--fill in C for {B, cane}.
B's row has only hats and gloves "open". And he's already got something from B and from C, so his hat and gloves must come from A and D. But D has his own gloves.... so B must have A's Gloves and that leaves B having D's hat. Fill in A for {B, gloves} and D for {B, hat}.
Do the same for A's row: A already has A's Coat, and D's cane, therefore his hat and glove belowng to B and C.... since C already has his own hat, A must have B's hat... and that mean A has C's gloves. Fill in B for {A, hat} and C for {A, gloves}.
D is the only one missing a hat, and A's is the only one not taken, so fill in A for {D, hat}. Similarly, C is the only one missing gloves, and B's are the only ones not taken, so fill in B for {C, gloves}.
And finally, C needs something from A, and D needs something from B and the canes are free... so fill in A for {C, cane} and B for {D, cane}.
Your whole grid should now be filled in with the appropriate information.
Cheers!
method of solving (also a spoiler)
