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SprngHlJn 01-23-2013 04:14 AM

I humbly request help
I believed myself to be quite good at these. Even though I never broke any speed records, I must admit I was rarely stumped.

Laughed, I did, when I saw an 11% success rate. "This shall be a fair test of my logical mettle!"

I was ... ill-prepared for what followed, and was summarily humbled.

Any help, or even a few pointers in the right direction would be much appreciated. I've included up to where I was defeated. But after so many second-guesses, they may not even be right.


zenobia43 01-23-2013 12:47 PM

That was a tough one. I got the following solution:

$6.99 - Gwendolyn - spaghetti - mushroom
$7.99 - Louis - capellini - arrabiata
$8.99 - Nathaniel - fusilli - pomodoro
$9.99 - Claudia - taglioni - marinara
$10.99 - Angie - farfalle - bolognese

On the first pass through the clues, it looked hopeless. I started working the intersections of rows and columns to get some positives.

You are missing an X from clue 6. $10.99 cannot be marinara. However, I didn't have the X that you have at $10.99 and arrabiata. Not sure how you got that one.

If you still have the unsolved game in the recent games list, try this solution to see what happens.

I can give a step by step if you want to take the time. This one has a situation where only two possibilities exist for two members of the same category. This allows you to X out those two possibilities for the other three members.

It also has several situations where the intersection of two elements of the grid is null which allows you to place another X.

I don't really know if I have the right solution. However, it seems to satisfy all the constraints, and it was fun getting there.

SprngHlJn 01-24-2013 04:42 AM

Thank you for being kind in saying the puzzle gave you problems as well.

The arrabiata/$10.99 contradiction I found was that whoever ordered arrabiata ordered capellini, and the person who ordered capellini cannot be the person who paid $10.99 because Nathaniel paid one dollar more than that person according to clue 4, and no one paid more than $10.99. Therefore, since arrabiata = capellini, and capellini /= $10.99, arrabiata /= $10.99. I spell this out not to insult your intelligence but to confirm my own hypothesis. I assure you this puzzle reduced the trust in my own logical ability immensely.

Concerning your other note, I was unsure whether I should follow exactly the grammar in clue 6. The phrase "was the runner" seemed to indicate that the first two conditions only applied to one person. Otherwise, the phrase would be "were the runners." I assumed, very possibly incorrectly, that this was simply a limitation of the program which generates these puzzles, and decided against further speculation. I understood clue 6 to say "The runner who ordered fusilli did not spend $10.99, nor chose marinara sauce." From this interpretation (which, again, may be entirely misguided), I'm unsure as to how the person who spent $10.99 could not have chosen marinara sauce. However, using that information, I solved the puzzle to your answer, and received

"You solved the puzzle correctly in 1 day, 10 hours, 16 minutes, 3 seconds. That's worth 10 points!" (which, if I am able to understand my error, will be the most valuable 10 points I've ever received from this site).

I fear I am missing something, as clearly your solution worked, but I am ignorant of how you achieved it given clue 6. I also readily admit that it may have nothing to do with grammar, and I am simply monumentally missing the point. Any clarification to this effect would be appreciated.

Also, thanks for your explanation and for taking the time to answer.

zenobia43 01-24-2013 11:21 AM

I see clue 6 as a variant of clue 5 where there is a list of elements that aren't the same person.

In clue 6, there are three elements in three different categories, so that should produce 3 Xs.

Many of the new puzzles have clues of this form.

In my opinion, this puzzle is tough because it requires repeated application of the more advanced deductive reasoning techniques. I like the new puzzles added in mid-December because many of them look so utterly hopeless after the first pass through the clues and then finally yield.

Thanks for verifying the solution.

SprngHlJn 01-24-2013 07:48 PM

Boy, this one took me down the rabbit hole.

To be honest, clue 6 was the one clue I kept striking-through and then clearing, so I suppose my subconscious was quite upset with my lack of attention.

For me, the clue was "Neither a nor b is c," and, as I said, I read it as "c is not a, nor is it b." Logically, however, the original formulation would be expressed as c→(a∨b), or "if c, then not a or b." The relationship between a and b, from that clue alone, is not specified, other than their sharing a property, i.e., not being c (which actually makes them slightly more likely to be equal).

But in looking at the grammar of the clue, at first there does seem to be a correlation. See this link for an interesting discussion of it at another puzzle site. As well, it sounds odd and redundant to include the subject twice if it is obviously the same, e.g., "Neither Wendy Watson nor Wendy Watson has blonde hair," though it is not grammatically incorrect. But if we're dealing with unknowns, as we are in these puzzles, it may not sound so odd. Imagine a reporter at the Daily Bugle is trying to figure out the identity of a certain webslinger. During the course of her investigation, she remarks "Neither the freelance photographer Peter Parker nor the amazing Spider-man reads Kierkegaard." If she were filling out a puzzle similar to ours, she could safely put an X in the Peter Parker/Kierkegaard intersection and in the Spider-man/Kierkegaard intersection. But to put an X in the Peter Parker/Spider-man intersection would make the puzzle unsolvable, as we all know Peter Parker is, in fact, the amazing Spider-man. Her original statement was correct (logically and grammatically), included the article "the" (a condition for contradiction stated in the other website) and expressed no clear redundancy, with both parts of the subject (Spider-man and Peter Parker) being identical.

However, as both you and the other website have noted, this does seem to be a necessary way to solve these puzzles, so I thank you again for pointing me in the right direction. Also, as my formal logic skills are in no way reliable, and my grammatical example included Spider-man, I may very well be missing something. Still, if I am right (and I am nowhere near confident enough to declare myself so), I hope this condition will be listed in the puzzle's rules.

If nothing else, I had a nice refresher in logical operators and I learned that in 'neither ... or' formulations, the verb tense agrees with the last of the list, the reason for which I now know.

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