My Christmas gift to all the dopers out there. Have fun figuring it out.
A group of merchants wants to put up matching Christmas decorations on their block, but they can’t agree on the color or the design. The possibilities are bells, festoons, stars, or wreaths in gold, green, red, or silver. The businesses are arranged as follows:
All the merchants on the north side of the street agree about gold or silver; i.e., either they all want gold or silver or they do not want all gold or silver.
Each merchant wants a different color and design; e.g., the only one who wants silver wreaths is the owner of the hardware store at #10.
The four merchants at the west end of the block want all designs except stars and all colors except gold.
The men’s and women’s clothing stores are directly across from each other; one owner wants gold and the other wants green.
The owners of the toy store and the children’s clothing store, which are next to each other, want different colors; one wants stars.
The two pairs of businesses that are farthest apart are the florist and the vegetable store, and the butcher and the bank. No two of the four want the same color or the same decoration.
The owners of the four middle establishments want all designs and colors.
The butcher, who doesn’t want silver, agrees with the bookstore owner in one respect and the luncheonette owner in the other; the fish-store owner, who doesn’t want bells, also agrees with the bookstore owner in one respect.
The middle businesses are the deli and the toy store on one side of the street and the hardware store and the luncheonette on the other.
The owners of the businesses at #5, #6, #7, and #8 all want different colors.
The drugstore and the shoe store are directly across from each other; the hardware store owner disagrees with the drugstore owner about color and with the shoe store owner about design.
Two clothing stores are adjacent.
The hardware store is not next to the stationery store but is closer to it than the drugstore. All three are on the same side of the street.
The vegetable store, whose owner wants wreaths, is next to the women’s clothing store.
Enjoy. evil laughter
– Sylence
I don’t have an evil side. Just a really, really apathetic one.
Fretful, I used # 2 as a freebie, and that led me to the eventual conclusion that in #13, the hardware store is closer to the stationary store than the hardware store is to the drugstore.
One thing I’m not clear on is does each merchant only get to pick one color and one design: frinstance, a merchant can’t say he/she wants to have red and green festoons, right?
You may want to check the wording of #1 - the choices it offers are not consistent enough to yeild a decent clue.
I guess I’m going to need a clarification here, because I keep running into a SNAFU that makes the problem unsolvable for me.
Sylence,
Please clarify clue number 1 and 13.
Here’s why.
(Some logical steps are skipped over.)
Given that #10 - Hardware Store - Silver Wreath is truth.
I interpreted clue 1 to say that North side wants all gold/silver on their side or NONE of the gold/silver on their side. By clue 2 then, all of the gold/silver would be on the south side.
The men’s and women’s clothing stores have to be #13 and #14, which left me with the Drug store at #4.
By clue 3, merchant #4 cannot be gold, so it must be silver (by my interpretation of clue 1). But it cannot be silver either because it cannot be the same as the hardware store (clue 11).
I frequently solve logic puzzles similar to this. It’s my experience that when I make a mistake like I have above, it’s because I mis-read or misinterpreted some of the clues. Set me straight.
As for #13, my bad. The hardware store is not next to the stationery store but is closer to it than TO the drugstore. That TO makes a difference and I missed it.
Missdavis102: Each merchant has picked out ONE color and ONE design.
Enright3: You found a mistake. That should be AGREES not disagrees. I’m sorry, I had two friends proof this just to make sure I didn’t make any mistakes, and somehow we all missed that one.
– Sylence
I don’t have an evil side. Just a really, really apathetic one.
Yoo Hoo, Syyyyleeeennce,
Where are you? I have to talk to you.
Since I’m still getting hung up on your *$%^&@#! logic puzzle, I want you to throw me a bone or two…
Clue 6, about the two pairs of businesses that are farthest apart… does that mean that if I determine (for example) the florist is merchant # 1, that the vegetable store is merchant #16? To rephrase the question: Does “farthest apart” mean opposite ends of the street AND across the street too? Are the butcher and bank on same side of the street or opposites?
Hey, Sylence! There’s something missing, my friend…
I’ve incorporated all the fixes you posted, but there’s still not quite enough information. As far as I can tell – and I’ve already spent WAY too much time on this thing – there is NO WAY to determine who’s in 13-16, and without that, the rest can’t fall into place, since 13’s choice of green has to be the key to the rest of the reds/greens.
Also, Clue 1. should be reworded; it doesn’t make a heck of a lot of sense the way it is. How about, “All the merchants on the north side of the street agree about gold and silver; i.e., they have agreed either that they all want gold or silver, or that none of them want gold or silver.”
I’ve been solving logic problems for a lot of years, and they’re a lot of fun! But only when all the clues are there…
I don’t know why fortune smiles on some and lets the rest go free…
Farthest apart does mean diagonally across the street, as in #1 and #16.
And there is enough information to solve this problem. I wouldn’t have posted it otherwise.
That said, #1 is a bit vague, so I’ll clarify-- the merchants on the north side have agreed that they want all gold and silver or no gold and silver at all on their side of the street. They want all gold and silver or all red and green, in other words.
– Sylence
I don’t have an evil side. Just a really, really apathetic one.
“6. The two pairs of businesses that are farthest apart are the florist and the vegetable store, and the butcher and the bank…”
OK, OK. Once the correct answer was posted, it became clear to me, but I can’t help pointing out that the wording I quoted above could be interpreted at least three different ways, only one of which will lead to the correct answer.
By the wording of the clue, the “two pairs” could have been 1/2 and 15/16, 1/15 and 2/16, OR 1/16 and 2/15. My previous post was a result of my incorrect – but legitimate – assumption that the pairs were 1/2 and 15/16.
I don’t know why fortune smiles on some and lets the rest go free…
