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Logic Challenge #11 - Buffalo Wings

by alisasommer Mon Jul 27, 2009 4:12 pm

Answers:
1. E
2. B
3. C
4. E
5. B
6. E
 
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Re: Fortnightly Logic Game #11 - Buffalo Wings

by lsatlifer Mon Jul 27, 2009 4:57 pm

This was a tough game, but I'll do my best to try to explain how I arrived at my answers:

I started with a diagram that looks like a much larger version of an asterisk, *, which has 6 sides. Image
My variables: G I J K L N and f m h (purposefully lower case, for distinction).

I numbered it in a clockwise fashion, and I placed J right at the top, since the rule says that's where he goes. then I draw the f for flaming next to the #4, to indicate that this person order flaming wings.

The key to this game is the distribution. But I'll start by explaining each rule.

1) no 2 people who sit next to each other have the same kind of wings. This means no ff, mm, or hh around our circle.

2) L sits across from G. This means that NEITHER L or G can sit in spot #4, because across from spot #4 is #1, which is J (rule 6) :-)

3) The person in #4 has f-wings. Great. This means that #5 and #3 CANNOT have f-wings because this will violate rule 1).

4) I and K can't sit next to each other.

5) hot wings is ordered more than anything else. this is the KEY to the game, in my opinion. This lets us know the distribution of sauces around the circle, if we combine this rule with rule 1. since there are only 6 spots, and each sauce must be ordered at least once, the if we were to distribute equally, then we can have the following distribution:2 -2 -2 for f - m - h, respectively. But this is NOT valid because we must have more h than f and more h then m. So we just have to steal one from m or f and end up with this distribution: 1 - 2- 3 OR 2-1-3.

The placement of the f in spot 4, precludes the possibility of being able to place these 3 h's anywhere on the circle. We know that h's can't be next to each other (from rule 2), so the only possible distribution of h's starts with spot #1, which is where J is (rule 6), and every other spot thereafter, spots #3 and #5.

6) J is in spot #1

And that's the game!

Now to the questions.

1) Typical "what's possible" question. Looking at my diagram, I know that J must order hot wings, so A and D are automatically eliminated. Then I hit the rules to see which other ones I can eliminate. C doesn't work because I and K are next to each other, which they shouldn't be. E doesn't work because G and L are not across from each other. This is a bit tough to see because you have to visualize the numbered spots, which helps if you've got a good diagram.

2) If N and I are next to G (on either side), then this puts major constraints on where the G-L combo can fit. Since G must be squeezed between N and I, then we know that G canNOT go in spots #6 or #2. So all that's left is #3 and #5 (remember spot #4 is impossible for G since J is across from #4, and L must be across from G). I tried both scenarios and noticed that I must always be above G in this scenario, if not, then I and K always end up being next to each other since N must be in spot #4 (remember g is constrained to spots #3 and #5). SO that leaves us with 2 scenarios. And thus B is the correct choice.

3) this is a universal question. You'll notice from the main diagram (if you have enough time to just study it for 30 seconds) that N cannot go in spots #2 or #6 because this will force I and K to be next to each other, given that L and G are across from each other. Thus, N can be in #3, #4, or #5, all of which already have sauces: h, f, and h, respectively. This leads us to choice C, which says that N can have mild wings. This is impossible because NONE of the spots where N can be are mild.

4) Following from #3, if N orders f-wings, then we know it's in spot 4, which is across from. Choice E. :-)

5) This was a scenario question, where I didn't see any other way to attack but to try each scenario. It helps to keep the distributions of sauces in mind. A doesn't work because milds can only be in spots #2 and #6, which are not across from each other, as G and L should be. B works because we can put I or K in the 4th spot and the other in, for example, the 6th spot. Stop there.

6) If G and L now have to be next to each other, then there are no longer any constraints on where it can be located. All we do know is that there will be 3 spots left, so as long as I isn't next to K, we're alright. Thus A is our choice.
Last edited by lsatlifer on Mon Jul 27, 2009 5:47 pm, edited 3 times in total.
 
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Re: Fortnightly Logic Game #11 - Buffalo Wings

by chilwoo Mon Jul 27, 2009 5:25 pm

I drew a circular diagram numbered 1-6 clockwise with two rows next to each number - with 1,4 2,5 and 3,6 opposite from each other. I put J at seat 1 and F at seat 4 as we are told. For abbreviating the other constraints -
Const. a (not)MM (not)HH (not)FF to show that adjacent seats cannot have same sauces
Const. b L _ _ G and G _ _ L to show that being opposite ends equals two spaces between
Const. d (not) KI (not) IK

Since there are more hot sauces than any other sauce and each sauce needs to be picked at least once, you can infer there are at least 3 hot sauces. Looking at my diagram, since seat 4 is F and we know adjacent seats cannot have same sauces, H needs to go at seats 1, 3, and 5. Seats 2 and 6 are either F or M (one of each).
Initial setup completed.

#1. Which one of the following represents a possible matching of people with the type of wings they order, listed in order from 1 through 6 according to the seats they occupy?
Eliminate using the constraints
No adjacent people order same sauce - eliminate D
Lucita across from Gary (i.e. two spaces in between) - eliminate E
Kim and Inga not adjacent - eliminate C
More hot wings than any other sauce - eliminate A
B correct answer

#2. If Inga and Niko both sit adjacent to Gary, how many different seating arrangements are possible?

Looking from a circular diagram perspective, we know that G can only go in slot 3 or 5, due to I and N being adjacent (J is adjacent to G if G is on 2 or 6). This provides two diagrams to work with: J _ G _ _ L (1-6 clockwise) and J L _ _ G _ (1-6 clockwise). For the first diagram, I must go in slot 2 because J N G I K L violates const. d. Therefore the order must be JIGNKL. The second diagram is similar with I needing to go in slot 6 leaving JLKNGI

This leaves two possible setups either way. B is correct

#3. Which one of the following CANNOT be true?
With the sauce order from 1-6 clockwise going, H F/M H F H M/F we go down the answer choices.
(A) Lucita orders hot wings.
L can go on space 5 or 3, so false
(B) Gary orders flaming wings.
G can go on space 2 or 6, so false
(C) Niko orders mild wings.
N can only go on space 3, 4, 5 because is N is on either 2 or 6, K and I will end up being adjacent. Since 3, 4, 5 are hot or flaming, we know that C is correct.


#4. If Niko orders flaming wings, which one of the following must be true?
Similar logic to question 3, since N can only go on 3, 4 or 5, if Niko orders flaming, he must be at seat 4. Therefore answer choice E Niko sits directly across from Jae.
must be true.

#5. 5. Which one of the following could be true?
Go down the answer choices
(A) Both Gary and Lucita order hot wings.
G and L cannot both be H, because either G or L must occupy space 2 or 6 and we know 2 and 6 can be either M or F.
(B) Both Inga and Kim order flaming wings.
I can place I and K at positions 2 and 4 (e.g. JKLING) spot 4 must be F and 2 can be F so B looks good here.
(C) Both Jae and Inga order mild wings.
J must must H so this doesn't work
(D) Both Inga and Kim order mild wings.
The only way this could be true is if I and K occupy slot 2 and 6. This is impossible because G and L could not be opposite each other. Doesn't work.
(E) Both Niko and Jae order flaming wings.
We know J must be H. Doesn't Work
Answer B

6. If the condition that Lucita sits directly across from Gary is changed to Lucita sits adjacent to Gary, and if all other conditions remain in effect, which one of the following is a complete and accurate list of the types of wings that Niko could order?


Using the new constraints, nothing changes on the sauce side of my diagram, so I tried to see if N could go on either 2 or 6, this way I could take out mild as an option.

JNILGK looked fine to me - since N can go into slot 2 both mild and flaming are options, eliminate C D E.
Now I am seeing if N can go into slot 3 or 5 to eliminate hot.
JINLGK also looks fine - so eliminate B, A is correct

I had initially got this question wrong because I tried to create frames, and assumed N could only go in spaces 3 or 5, but I realized that was incorrect.

Guys please let me know if I screwed up anything!
 
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Re: Fortnightly Logic Game #11 - Buffalo Wings

by stackoutawinner Mon Jul 27, 2009 6:59 pm

The following attachment is a LINEAR solution using the 3D solution type.

Answers are as follows:
B
B
C
E
B
A
Attachments
Buffalo Wing Linear Solution.pdf
(15.15 KiB) Downloaded 500 times
 
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Re: Fortnightly Logic Game #11 - Buffalo Wings

by stackoutawinner Mon Jul 27, 2009 7:58 pm

Additional Question #1.

If we change the constraint disallowing I & K to sit adjacent to that they MUST sit adjacent, and all other constraints apply, what is a complete and accurate list of sauces that N can order?

(A) mild, hot, flaming
(B) mild, flaming
(C) hot, flaming
(D) mild, hot
(E) hot

For a bonus, list out the possible sauces that Inga can order.

Solution attached.
Last edited by stackoutawinner on Mon Jul 27, 2009 8:07 pm, edited 1 time in total.
 
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Re: Fortnightly Logic Game #11 - Buffalo Wings

by yetemlion Mon Jul 27, 2009 8:06 pm

Alright.

Answers:
1. B
2. B
3. C
4. E
5. B
6. A
Bonus Question#1: B (And the only possible sauces that Inga can order are Flaming or Hot in this first bonus question)
Bonus Question#2: D
Bonus Question#2-2: E

Bonus Question 3-1: A
Bonus Question 3-2: C (?)
Bonus Question 3-3: D
_____________________
The easiest way to solve this mapping game is through a few simple steps.
1. Draw the following diagram:

2-----1-----6



3-----4-----5

(imagine a circle is in the middle of these parallel lines, connecting all six members)

NOTE: 2 and 3 are ADJACENT while 3 and 6 are ACROSS from eachother

RULES:
1- L---G (therefore, Lucita and Gary can only be in 2 and 5 or 3 and 6, since these are the only spots that are across from each other, and 4 is across from where Jae is sitting)
2- 4 = Flaming sauce
3- K/I and I/K
4- there must always be 3 hot wings in order for hot wings to be the most used sauce
5- Jae = 1


Now, to add in the rules and make deductions


2 (F/M)-----1(J:H)------6(F/M)



3(H)--------4(F)----------5(H)
____________________________
Question #1: B-
This is the only on which would work because here there are three hot sauces, Lucita is directly across from Gary, Kim is not adjacent to Inga and no one sauce is adjacent to another sauce of the same kind.
2 (L:M)-----1(J:H)------6(K: M)



3(N:H)--------4(I:F)----------5(G:H)

Question #2. B
Garry can only be in spots 3 or 5 because he cannot be adjacent to Jae, he must be adjacent to Inga and Niko. Inga must be in 6 or 2 and Niko must remain in 4 so that Lucita can be directly across from Gary and Kim will not be adjacent to Inga.
Scenario 1
2 (L: F/M)-----1(J:H)------6(I:F/M)



3(K:H)--------4(N: F)----------5(G:H)

or
Scenario 2
2 (I: F/M)-----1(J:H)------6(L:F/M)



3(G:H)--------4(N: F)----------5(K:H)

Question#3: C
Niko cannot order Mild wings, which would put him in spot 2 or 6 because it would result in the following scenario:
2 (N: F/M)-----1(J:H)------6(L/G:F/M)



3(G/L:H)--------4(L/K: F)----------5(L/K:H)

This scenario results in L being adjacent to K.

Question#4: E
If Niko orders flaming wings he must sit across from Jae in order to allow Lucita to be directly across from Gary and to prevent Inga from being adjacent to Kim.
2 (L: F/M)-----1(J:H)------6(K/I:F/M)



3(I/K:H)--------4(N: F)----------5(G:H)



Question#5: B
Both Inga and Kim can order flaming wings in the following scenario:
2 (K/I: F/M)-----1(J:H)------6(L/G:F/M)



3(G/L:H)--------4(I/K: F)----------5(N:H)

Question#6: A
If Lucita must sit adjacent to Gary then the following scenarios are the resulting options, which allow Niko to have mild, hot, or flaming sauce.
Scenario 1
2 (L/G: F/M)-----1(J:H)------6(I/K:F/M)



3(G/L:H)--------4(I/K: F)----------5(N:H)

Scenario 2
2 (I/K: F/M)-----1(J:H)------6(L/G:F/M)



3(N:H)--------4(I/K: F)----------5(L/G:H)

Scenario 3
2 (I/K: F/M)-----1(J:H)------6(N:F/M)



3(G/L:H)--------4(L/G: F)----------5(I/K:H)

Scenario 4
2 (N: F/M)-----1(J:H)------6(I/K:F/M)



3(I/K:H)--------4(L/G: F)----------5(G/L:H)

Bonus Question #1: B
Niko can only have Flaming or Mild sauce in this scenario, and Inga can only have flaming or hot sauce, depending on if she is in spot 3, 4, or 5.
Scenario 1
2 (G/L: F/M)-----1(J:H)------6(N:F/M)



3(I/K:H)--------4(I/K: F)----------5(G/L:H)

Scenario 2
2 (N: F/M)-----1(J:H)------6(G/L:F/M)



3(G/L:H)--------4(I/K: F)----------5(I/K:H)

Bonus Q #2-1: D
If the condition that Lucita sits directly across from Gary is changed to Lucita cannot sit adjacent to Gary, but Kim must sit directly across from Jae, and if all other conditions remain in effect, then which of the following could be true EXCEPT:

There are three possible scenarios that work given the constraints above. I none of these scenarios (as are shown below) can both Inga and Niko order flaming wings simultaneously. In Scenario 1 and 2, Inga can order flaming wings, however, Niko can only order hot wings. In Scenario 3, both Inga and Niko cannot order flaming wings because then no one would be ordering mild wings, which goes against one of the basic constraints that each of the sauces must be used by at least one person.


Scenario 1
2 (I: F/M)-----1(J:H)------6(G/L:F/M)



3(G/L:H)--------4(K: F)----------5(N:H)

Scenario 2
2 (G/L: F/M)-----1(J:H)-------6(I:F/M)



3(N:H)-----------4(K: F)----------5(G/L:H)

Scenario 3
2 (I/N: F/M)-----1(J:H)-------6(I/N:F/M)



3(G/L:H)-----------4(K: F)----------5(G/L:H)

Bonus Q #2-2: E
Assuming the same conditions as the previous question, which of the following CANNOT be true?

As the previous three scenarios prove, which are the only possible scenarios given the constraints, Inga cannot sit next to Jae and Niko.

Bonus Question 3-1: A
If the condition that hot wings are ordered more than any other type of wing is changed to hot wings are ordered less than any other type of wing and Kim orders mild wings along with one other person, and if all other original conditions remain in effect, which one of the following is a complete and accurate list of the types of wings that Niko could order?
Scenario 1
2(L/G: F)-----1(J:M)------6(I:F)



3(K:M)------4(N: F)--------5(L/G:H)
Scenario 2
2(I: F)-----1(J:M)------6(L/G:F)



3(L/G:H)------4(N: F)--------5(K:M)

Scenario 3
2(I: F)-----1(J:H)------6(L/G:F)



3(L/G:M)------4(N: F)--------5(K:M)

Scenario 4
2(L/G: F)-----1(J:H)------6(I:F)



3(K:M)------4(N: F)--------5(L/G:M)

Niko can only have flaming sauce because must take spot four which has flaming sauce.

Bonus Question 3-2: C (?)
Assuming the same conditions as the previous question, all of the following could be true EXCEPT:
C. Jae orders mild wings while Inga orders hot wings
D. Inga orders hot wings while Gary orders mild wings
I am not entirely sure about this question. I found no scenario in which Inga could order hot wings.

Bonus Question 3-3: D
Assuming the same conditions as the previous two questions except that Niko cannot sit adjacent to Lucita, which one of the following is a complete and accurate list of the types of wings that Gary could order?
Scenario 1
2(L: F)-----1(J:H)------6(I:F)



3(K:M)------4(N: F)--------5(G:M)
Scenario 2
2(I: F)-----1(J:H)------6(L:F)



3(G:M)------4(N: F)--------5(K:M)
Scenario 3
2(L: F)-----1(J:M)------6(I:F)



3(K:M)------4(N: F)--------5(G:H)
Scenario 4
2(I: F)-----1(J:M)------6(L:F)



3(G:H)------4(N: F)--------5(K:M)

Gary can have hot or mild sauce.
Last edited by yetemlion on Thu Jul 30, 2009 12:46 am, edited 10 times in total.
 
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Re: Fortnightly Logic Game #11 - Buffalo Wings

by stackoutawinner Tue Jul 28, 2009 12:06 am

BONUS QUESTION #2

I wanted to come up with a situation that would make me think a bit. Solutions attached. Hope you enjoy...

Bonus Q 2-1
If the condition that Lucita sits directly across from Gary is changed to Lucita cannot sit adjacent to Gary, but Kim must sit directly across from Jae, and if all other conditions remain in effect, then all of the following could be true EXCEPT:

A. Niko orders hot wings
B. Both Gary and Inga order mild wings
C. Neither Gary nor Lucita order mild wings
D. Both Inga and Niko order flaming wings
E. Both Gary and Jae order hot wings

Bonus Q 2-2
Assuming the same conditions as the previous question, which of the following CANNOT be true?
A. Kim sits next to Niko and Lucita
B. Inga sits next to Jae and Lucita
C. Jae sits next to Niko and Inga
D. Gary sits next to Niko and Kim
E. Inga sits next to Jae and Niko
Last edited by stackoutawinner on Tue Jul 28, 2009 11:10 am, edited 1 time in total.
 
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Re: Fortnightly Logic Game #11 - Buffalo Wings

by Lsat Tue Jul 28, 2009 1:55 am

1. B
2. B
3. C
4. E
5. B
6. A

Exactly six people"”Gary, Inga, Jae, Kim, Lucita, and Niko"”sit around a circular table at a restaurant. The six seats at the table are numbered 1 through 6 such that seat 1 is directly across from seat 4, seat 2 is directly across from seat 5, and seat 3 is directly across from seat 6. Each of the six people places an order for exactly one plate of buffalo wings with exactly one of three types of buffalo sauce: mild, hot, flaming. Wings with each of the sauce types are ordered by at least one person. The following conditions apply:

* No two people who sit adjacent to one another order wings with the same type of sauce.
* Lucita sits directly across from Gary.
* The person who sits in seat 4 orders flaming wings.
* Kim and Inga do not sit adjacent to each other.
* Hot wings are ordered more than any other type of wing.
* Jae sits in seat 1.


I started this game by building a backbone of the characters (G, I, J, K, L, N), and drawing a circle w/ 1-6 clockwise beginning at 12 o'clock (Sorry, my ASCII art is rusty). As I read each rule I abbreviated it (ie, Same sauce not adj., L------>G, #4=Flm, [KI] w/a slash, Hot = 3x, Mild = 1 or 2, Flm = 2 or 1) and added it to my diagram if I could, then condensed rules and found applicable contrapositives (Same sauce not adj + Hot 3x = Hot in 1, 3, 5) and added that information to my master diagram.

_____________Jae
_____________ Hot
____________ xxxxxxx
_________ xxx __ 1 __ xxx
_______ xxx 6 _______ 2 xxx
_____ xx ________________ xx
____Hot xxx 5 _______ 3 xxx Hot
_________ xxx __ 4 __ xxx
____________ xxxxxxx
____________ Flaming

Then I tackled the questions.

1. Which one of the following represents a possible matching of people with the type of wings they order, listed in order from 1 through 6 according to the seats they occupy?

(A) Jae: mild; Gary: flaming; Kim: hot; Niko: flaming; Lucita: hot; Inga: mild
(B) Jae: hot; Lucita: mild; Niko: hot; Inga: flaming; Gary: hot; Kim: mild
(C) Jae: hot; Niko: mild; Lucita: hot; Inga: flaming; Kim: hot; Gary: flaming
(D) Jae: flaming; Lucita: mild, Kim: hot; Niko: flaming; Gary: hot; Inga: hot
(E) Jae: hot; Inga: flaming; Gary: hot; Niko: flaming; Lucita: hot; Kim: mild

Knowing that Jae ordered Hot sauce I could immediately dismiss options A (Jae Mild) and D (Jae Flaming). Then I checked which rules were broken by each remaining option. C has Kim and Inga sitting next to each other which is forbidden and E doesn't have Gary across from Lucita which is required leaving option B as the only possible solution.

2. If Inga and Niko both sit adjacent to Gary, how many different seating arrangements are possible?

(A) one
(B) two
(C) three
(D) four
(E) five

Since Gary has to sit across from Lucita he cannot be in seat 1 which is occupied by Jae, or seat 4 which is across from Jae. This new rule states that Inga and Nico are each flanking Gary, which means he cannot be sitting in seats 6 or 2 because they are each next to Jae, leaving seats 3 and 5 as the only possible seats for Gary. If Gary sits in seat 3 that per the rules, Lucita must be sitting in seat 6 directly across from Gary. The rules state that Kim and Inga cannot be next to each other so Nico must be in position 4, Inga is in position 2 and Kim is in position 5. This is the only possible configuration when Gary is in seat 3. Move Gary to seat 5 and the entire grid simply reverses itself to the only possible option (Jae=1, Lucita=2, Kim=3, Nico=4, Gary=5 and Inga=6). Thus the correct answer is B, two.

3. Which one of the following CANNOT be true?

(A) Lucita orders hot wings.
(B) Gary orders flaming wings.
(C) Niko orders mild wings.
(D) Gary orders mild wings.
(E) Kim orders flaming wings.

This is probably the easiest problem in the set. I just started at the top and went until I found an impossibility. Lucita sits across from Gary which means they are in 2--5 or 3--6 either of which allows for Lucita to order Hot wings or Gary to order Flaming ones. However, since the only possible seats with the option of ordering Mild wings are seats 2 and 6 (please see my fine ASCII art diagram above), Nico cannot possibly order Mild wings since either Kim or Inga (whom you'll recall cannot sit next to each other) must sit in the lone seat (2 or 6) between Jae and either Gary or Lucita, which are the only seats able to order the Mild wings. Since the question is asking for an impossibility, circle answer C and move along.


4. If Niko orders flaming wings, which one of the following must be true?

(A) Lucita sits adjacent to Jae.
(B) Gary sits adjacent to Niko.
(C) Inga sits adjacent to Lucita.
(D) Niko sits directly across from Kim.
(E) Niko sits directly across from Jae.

This question builds on the information from question 3. We already know that Nico cannot sit in seats 2 or 6, so if he orders Flaming wings he must be sitting in seat 4, directly across from Jae in seat 1 which is the option given in answer E.


5. Which one of the following could be true?

(A) Both Gary and Lucita order hot wings.
(B) Both Inga and Kim order flaming wings.
(C) Both Jae and Inga order mild wings.
(D) Both Inga and Kim order mild wings.
(E) Both Niko and Jae order flaming wings.

Since this is a "could be true" question we must find the "not impossible" answer. Start at the top and test each possible answer until encountering one that is not impossible. We already know from the diagram that the only seats that ordered Hot wings are 1, 3 and 5 none of which is directly across from the other so option A is impossible. Inga and Kim aren't allowed to sit next to each other which means that one of them must be sitting in the lone spot between Jae and either Lucita or Gary (refer back to question 3 for an explanation of how this works) which can order either Mild or Flaming wings. The other (Inga or Kim) who is not in the 2/6 seat must be in either 3, 4 or 5 which offer only Hot or Flaming. Thus, it is possible for Inga and Kim to both order Flaming wings (B), but impossible for them both to order mild wings (D). We know from the set up that Jae is in seat 1 and that seat 1 orders Hot wings, so C and E are both impossible leaving answer B as the only "not impossible" answer.


6. If the condition that Lucita sits directly across from Gary is changed to Lucita sits adjacent to Gary, and if all other conditions remain in effect, which one of the following is a complete and accurate list of the types of wings that Niko could order?

(A) mild, hot, flaming
(B) mild, flaming
(C) hot, flaming
(D) mild, hot
(E) hot

This question changes the rule that Gary has to sit across from Lucita to Gary sits next to Lucita which means that none of our previous work can help with determining the answer. If we imagine Gary and Lucita sitting in seats 2 and 3, then Kim and Inga (who still cannot sit next to each other) must be in seats 4 and 6 leaving Nico in seat 5 with the Hot wings. If we move the Gary + Lucita pair to seats 3 and 4, it is now possible for Kim to be in seat 2, Inga to sit in seat 5 and Nico to sit in seat 6 which can order its choice of Mild or Flaming wings, thus A must be the answer.
 
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Re: Fortnightly Logic Game #11 - Buffalo Wings

by adam.kobler Tue Jul 28, 2009 9:10 am

Code: Select All Code
Rule 1)  No two people who sit adjacent to one another order wings with the same type of sauce.
Rule 2) Lucita sits directly across from Gary.
Rule 3) The person who sits in seat 4 orders flaming wings.
Rule 4) Kim and Inga do not sit adjacent to each other.
Rule 5) Hot wings are ordered more than any other type of wing.
Rule 6) Jae sits in seat 1.


I made a few inferences from this.

From Rule 2, I concluded that there were only two ways the game could go.
The GL (Gary and Lucita) pair is either in 2,5 or or 3,6 (in no particular order). GL can not be 1,4 since J is already sitting in seat one.

From Rule 5, I concluded that there must be at exactly 3 orders of hot wings. We can't have 4,5, or 6 orders, since it would result in "hot wing" people sitting next to other "hot wing" people and violate rule 1. We have to have more than 1 order of hot wings, obviously, and if we only have two orders, then either Mild or Flaming will have more, or everyone has 2/2/2, and that violates rule 5. Again, this limits us to 3 Hot.

Continuing from that inference, we have to put the hot wings in seat 1, 3, and 5. We need a seat between each, as per rule 1, and we can't put it in 2, 4, 6, since Rule 3 tells us 4= Flaming.

1=Hot 2=? 3=Hot 4=Flaming 5= Hot 6=?


Question 1:

Process of Elimination
A) Violates rule 1, since seats 1+6 have mild. (In a circle table, they're sitting next to each other!)
C) Inga is in seat 4 and Kim is in seat 5! Rule 4 warns us that this could end badly!
D) Violates rule 1, Seats 5 and 6 both have hot sauce!
E) Gary is in seat 3, but Lucita is in seat 5!

B is kosher!


At this point, I started to diagram the game

Option A (GL are 2 and 5, in some order. This leaves INK in 3,4,6 in some order)
Option B (GL are 3 and 6, in some order. This leaves INK in 2,4,5 in some order)

Forgive the crudity of the drawings, they're better in person!
Image




Question 2:
For this question, we have to put I and N next to G.
If we try this with option A (the first diagram), we see:
i) G has to sit in seat 5 (since to put him in seat 2 would have J in the way).
-this means L is in 2.
ii) With G in 5, I and N are in 4/6 (in either order), and K is in 3.
iii) But with K in 3, we can't have I in 4. So I sits in 6, and N sits in 4.
Clearly, Option A leaves us with only one seating possibility. (JLKNGI)


If we try this with option B (the second diagram), we see:
i) G has to sit in seat 3 (since to put him in seat 6 would have J in the way).
-this means L is in 6.
ii) With G in 3, I and N are in 2/4 (in either order), and K is in 5.
iii) But with K in 5, we can't have I in 4. So I sits in 2, and N sits in 4.
Clearly, Option B leaves us with only one seating possibility. (JIGNKL)

So we have possibilty from diagram A, and one from diagram B.
Total possibilities = 2. Answer B.


Question 3 -
For this one, I noticed that (ignoring J, who we know sits in seat 1 with hot wings), we have two groups. We have G and L, and then we have I/K/N.

No matter which diagram we use, the G/L pair will have one person with Hot, and one with Mild or Flaming.

No matter which diagram we use, the I/N/K group , one person with have Hot, one person will have Flaming, and one person will have either Flaming or Mild. The important thing to remember is that two of these three can't sit next to each other.

Option A:
I/N/K are 3/4/6. Since I and K can't be next to each other, they can't be 3/4. So N has to be in 3/4. This means that N will have Hot or Flaming.

Option B:
I/N/K are 2/4/5. Since I and K can't be next to each other, they can't be 4/5. So N has to be in 4/5. This means that N will have Flaming or Hot.

Based on this we see that N can NOT have mild wings, and thus answer C must be false, and is the correct answer.



Question 4:
We've established in question 3 that N will either be in (3 or 4) or (4 or 5). Seat 3 and 5 are hot wings. So if N has flaming wings, he has to be the person mentioned in seat 4 (Rule 3). Seat 4 is across from Seat 1, where J is sitting. Hence, answer is E.


Question 5:
As we discovered in question three, G and L will never have the same kind of wings. One will have H, and one will not. This eliminates option A. Since we've established that seat 1 (J) is having hot wings, this elimates option C and E. Also, we've established that in the "I/N/K" group, there will be one Hot and one Flaming, and one either Mild or Flaming. There is no way that two of them (I and K) can both have mild. This eliminates D. Thus, B is the answer.

Question 6:
This question was a bit harder, since it requires redrawing the game board.

Some basic things to keep in mind.
- J is still in 1. This hasn't changed.
- Two sequential seats will be used for GL
- This leaves I/N/K in the remaining three seats. Either sequentially (With N in the middle), or split up (with GL in the middle)

So, with J in 1, we can put the I/N/K group in either
A) 4/5/6 (leaving GL in 2/3)
B) 2/5/6 (leaving GL in 3/4)
C) 2/3/6 (leaving GL in 4/5)
D) 2/3/4 (leaving GL in 5/6)

Now, to isolate N and look at his possibilities, we need to see if we can figure out where he is sitting, and luckily, we can (mostly).

options A and D have INK sitting in a row. If either of these are the case, N must be in the middle. In either case, this leaves us with N sitting in seat 3 or 5, and eating hot wings. (As established at the beginning of the game, 1,3,5 are hot wing seats).

Options B and C, however, are much less restrictive. With INK split up, the only thing we can't do is put N in the seat away from the other two. We can not, for example, put N in 2 and leave I/K in 5/6. So in option B, N can sit in either 5/6, and all will be right with the world. With option C, N can sit in 2/3, and everyone is happy. So either way, we can either put N in 2 or 6, and he can have mild wings or flaming wings.

Since he can have Hot Wings with some of the seating options, and Mild or Flaming with the other two options, we choose A, since he can have any of the three wing sauces.
Last edited by adam.kobler on Tue Jul 28, 2009 8:13 pm, edited 1 time in total.
 
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Re: Fortnightly Logic Game #11 - Buffalo Wings

by dan Tue Jul 28, 2009 12:57 pm

Thanks for the responses everyone. These look great so far. Give me a chance to look through these. I'll be back...

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Re: Fortnightly Logic Game #11 - Buffalo Wings

by dan Tue Jul 28, 2009 1:36 pm

These explanations are really great so far. I'll encourage you guys to read each other's work. If you did the game in circle form, check out Stack's approach -- he actually used a linear form and had success. Good to see multiple approaches.

Stacks has also written some good bonus questions. Exercise your chops on those.

Feel free to ask any questions in here if you have them. Again, great work!
 
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Re: Fortnightly Logic Game #11 - Buffalo Wings

by adam.kobler Tue Jul 28, 2009 6:00 pm

dan Wrote:These explanations are really great so far. I'll encourage you guys to read each other's work. If you did the game in circle form, check out Stack's approach -- he actually used a linear form and had success. Good to see multiple approaches.


I was thrilled to see that someone else does circle-type questions in a linear diagram :)
 
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Re: Fortnightly Logic Game #11 - Buffalo Wings

by dan Tue Jul 28, 2009 6:29 pm

adam.kobler Wrote:
dan Wrote:These explanations are really great so far. I'll encourage you guys to read each other's work. If you did the game in circle form, check out Stack's approach -- he actually used a linear form and had success. Good to see multiple approaches.


I was thrilled to see that someone else does circle-type questions in a linear diagram :)


I agree. I prefer to use a circle arrangement, but there's no one right way to do these games. There are good and bad ways to be sure, but certainly there are multiple good ways.
 
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Re: Fortnightly Logic Game #11 - Buffalo Wings

by stackoutawinner Wed Jul 29, 2009 7:18 pm

The circular diagram is quicker, but you have to train yourself in it. The advantage of the linear diagram is that it resembles our typical number line. Either way, with circular constraints and a circular set up, it requires some practice if you're to solve these with both speed and accuracy.

This is why I horsed around with some other rule changes and came up with a third set of questions! (Hey, what can I say, I need the practice seeing how the various rules alter the game)...

Bonus Question 3-1
If the condition that hot wings are ordered more than any other type of wing is changed to hot wings are ordered less than any other type of wing and Kim orders mild wings along with one other person, and if all other original conditions remain in effect, which one of the following is a complete and accurate list of the types of wings that Niko could order?

A. Flaming
B. Mild
C. Flaming, mild
D. Mild, hot
E. Flaming, hot, mild

Bonus Question 3-2
Assuming the same conditions as the previous question, all of the following could be true EXCEPT:

A. Jae orders hot wings while Gary orders mild wings
B. Gary orders mild wings while Lucita orders flaming wings
C. Jae orders mild wings while Inga orders hot wings
D. Inga orders hot wings while Gary orders mild wings
E. Gary orders mild wings while Inga orders flaming wings


Bonus Question 3-3
Assuming the same conditions as the previous two questions except that Niko cannot sit adjacent to Lucita, which one of the following is a complete and accurate list of the types of wings that Gary could order?

A. Flaming
B. Mild
C. Flaming, mild
D. Mild, hot
E. Flaming, hot, mild

Linear solution is attached. If you want, I can write out a circular solution to all these and scan it in, but the linear is easier to type out.
 
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Re: Fortnightly Logic Game #11 - Buffalo Wings

by dan Thu Jul 30, 2009 11:40 am

Thanks, Stacks!

Any takers?
 
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Re: Fortnightly Logic Game #11 - Buffalo Wings

by adam.kobler Sun Aug 02, 2009 4:57 pm

stackoutawinner Wrote:Linear solution is attached. If you want, I can write out a circular solution to all these and scan it in, but the linear is easier to type out.


dan Wrote:Thanks, Stacks!

Any takers?



Yay! I tried, and got all three correct in a rather short time. I made the same inferences Stack did, in a slightly different order, and the questions fell into place.

Does this board have [spoiler] spoiler tags [/spoiler] ?

Edit: Looks like it doesn't. Darn. It's something the admins might want to look into if it's easy to add. Anything contained within spoiler tags is hidden from view by a black block until highlighted over with the mouse. It's super-useful, and would be awesome here.
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Re: Fortnightly Logic Game #11 - Buffalo Wings

by noah Sun Aug 02, 2009 11:08 pm

adam.kobler Wrote:
stackoutawinner Wrote:Linear solution is attached. If you want, I can write out a circular solution to all these and scan it in, but the linear is easier to type out.


dan Wrote:Thanks, Stacks!

Any takers?



Yay! I tried, and got all three correct in a rather short time. I made the same inferences Stack did, in a slightly different order, and the questions fell into place.

Does this board have [spoiler] spoiler tags [/spoiler] ?

Edit: Looks like it doesn't. Darn. It's something the admins might want to look into if it's easy to add. Anything contained within spoiler tags is hidden from view by a black block until highlighted over with the mouse. It's super-useful, and would be awesome here.

Thanks -- maybe just choosing a very light font color works? Ah, yes it does; take a look: secret message: destroy the LSAT
 
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Re: Logic Challenge #11 - Buffalo Wings

by redwan.saleh91 Mon Sep 22, 2014 2:28 pm

Just wondering,

why is the distribution of the 3 Hs, #1, #3, and number #5?

In my diagram, I have 3 Hs in #1, #3, and either #5 or #6.
For instance, if it's number 6 where the third H goes, then 5 which has a F next to it in #4, has to have M. I see that has totally acceptable.

Am I missing something or is this a mistake?

Thanks,
Red
 
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Re: Logic Challenge #11 - Buffalo Wings

by redwan.saleh91 Mon Sep 22, 2014 2:32 pm

Hi all,

I just saw my mistake -- wow, totally ignored the circular pattern of the seats -- which makes seat 6 unaccetable for H.

so it must be H in 1,3, and 5.

Thanks anyway.

Best,
Red