Last Saturday morning, Mrs. Holly returned the Christmas gifts for her children that hadn't worked out to the mall stores where she bought them. As it turned out, there was one return for each of the five children, including Ben, with each being returned for a different reason to a different mall retailer, one to Eddie Bauer. Given the details of her trip below, can you determine the order 1st-5th in which Mrs. Holly made the returns: the store visited, the child whose gift was returned, the item returned, and the reason for the return?

Mrs. Holly made these five returns (not necessarily in order): Zach's gift, the jeans, the article bought at Banana Republic, the item of apparel that the recipient didn't like, and the one to the 5th store in the order. Erica's gift, which wasn't the one returned because it was too small, wasn't the one purchased at American Eagle Outfitters.

Immediately after returning the hat to one mall store, Mrs. Holly returned Mindy's gift to another retailer. The item returned to Abercrombie and Fitch wasn't the one that was too large.

The article Mrs. Holly took back to Banana Republic, which wasn't Erica's, wasn't the one that was the wrong color.

Immediately after returning Tara's gift, Mrs. Holly returned the item that was too small; immediately after returning the too small article, Mrs. Holly returned the sweatshirt.

The shorts weren't the too large item. Mindy's gift wasn't the one returned because it was the wrong style. The item of apparel returned to the Gap, which wasn't Mindy's, wasn't the sweatshirt. Mrs. Holly didn't return the jacket to American Eagle. The jeans weren't Tara's.

In consecutive order first-to-last, Mrs. Holly made these three returns: the one to the Gap, Erica's gift, and the article that was the wrong color.

I know that this is a really old problem, but I thought I’d offer up an idea on how to approach it without massive trial and error.

There are two clues that involve "three consecutive returns," as well as another clue that involves "two consecutive returns." The two clues with three consecutive returns have to at least overlap a little. I want to see if I can line them up and find contradictions. Then I’ll see how the clue with two consecutive returns fits in.

With the least overlap we could have:
Tara, Small, Sweatshirt & Gap, Erica, Color - contradiction! (Gap wasn’t the sweatshirt.)
Gap, Erica, Color & Tara, Small, Sweatshirt - could be.

Most overlap:
Tara & Gap, Small & Erica, Sweatshirt & Color - contradiction! (Erica’s wasn’t too small.)
Therefore Tara’s was not bought at the Gap, and the Sweatshirt wasn’t returned due to its color.

Medium overlap:
Tara, Small & Gap, Sweatshirt & Erica, Color - could be.
Gap, Erica & Tara, Color and Small, Sweatshirt - contradiction! (Can’t have two people or two reasons on the same gift.)

So we found two arrangements that don’t have a contradiction so far. Now let’s see how the clue with two consecutive returns fits in.

Gap, Erica, Color & Tara, Small, Sweatshirt
"Hat, Mindy" can’t be 1&2 - then we’d have Erica and Mindy together
"Hat, Mindy" can’t be 2&3 - then we’d have Tara and Mindy together.
But "Hat, Mindy" as 3&4 or 4&5 would be legal so far.

?, Tara, Small & Gap, Sweatshirt & Erica, Color, ?
(the question marks are just stand-ins since I don’t know if Tara is 1st or 2nd)
"Hat, Mindy" can’t be 0&1 - then we’d have Tara and Mindy together.
"Hat, Mindy" can’t be 1&2 - then we’d have Mindy at the Gap which is disallowed in another clue.
"Hat, Mindy" can’t be 2&3 - then we’d have Erica and Mindy together.
"Hat, Mindy" can’t be 3&4 - then we’d have Hat and Sweatshirt together.
But "Hat, Mindy" as 4&5 would be legal so far.

So there is a total of 3 arrangements that don’t have contradictions yet.

A) Mrs. Holly returned…
1: To the Gap
2: Erica’s gift
3: Tara’s Hat for being the wrong Color
4: Mindy’s gift for being too Small
5: The Sweatshirt

B) Mrs. Holly returned…
1: To the Gap
2: Erica’s gift
3: Tara’s gift for being the wrong Color
4: The Hat for being too Small
5: Mindy’s Sweatshirt

C) Mrs. Holly returned…
1: Tara’s gift
2: To the Gap for being too Small
3: Erica’s Sweatshirt
4: The Hat for being the wrong Color
5: Mindy’s gift

My next steps would be to try to work though each one until I find a contradiction or a solution. Is this trial and error? Kind of, yes. But I think I used some logic to greatly minimize what I would be checking.

In both cases (A) and (B), Banana Republic has to be fourth.  Banana Republic can’t be 1st because that’s already the Gap, it can’t be 5th because of the first clue, it can’t be 2nd because that wasn’t Erica’s gift, and it can’t be 3rd because that wasn’t the "wrong Color" gift.

Also in both cases (A) and (B), Zach must be 1st.  In case (A) he can only be 1st or 5th, but 5th is eliminated by the first clue.  In case (B) he can only be 1st or 4th, but 4th is Banana Republic so it is eliminated by the first clue.

And again in both cases (A) and (B), Erica must have the jeans.  In both cases the jeans can't be 1st because of Zach and the first clue, they can't be 3rd because they weren't Tara's, they can't be 4th because of Banana Republic and the first clue, and they can't be 5th because of the first clue.

So who had the gift they didn’t like? It can't be 1st because of Zach and the first clue, it can't be 2nd because of the Jeans and the first clue, it can't be 3rd because it's already the wrong Color, it can't be 4th because it's already too Small, and it can't be 5th from the first clue.

So this is the contradiction that eliminates both cases (A) and (B).

 

Working through C, we end up getting the posted solution with no contradictions.

Posted by nikki on 2004-11-18 16:45:58