- 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!
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.