Q13

[velvet]

Doing this game real-time, I skipped over this question because I thought I missed some big inference about one element that must be in. When I went back to it, I used the orientation question (#12) to eliminate answer choices (b),(c),(d) since the answer to #12 did not have G,N,V in (I don't know how smart that was since this question asks of the two elements, 1 must be selected...but I did it anyway and it worked out). So down to (a) and (d), I looked at my previous work again and got to correct answer (d) since in number #15 I did not have F in.

In short, what's the correct way to get to the answer? I felt like this question was testing some kind of inference you were supposed to make.

[ohthatpatrick]

You are right on two counts:
1. This question does definitely reward people who made a pretty big inference from the outset.
2. Your method of eliminating answers from Q13 based on the correct answer to Q12 was not legit.

Let's start with the 2nd one. The correct answer to Q12 showed us this as our IN column: F, O, P, T, W

For Q13, we're analyzing whether we MUST select "at least one" of the two letters in each answer choice.

How do you test MUST BE TRUE answers? You see if the opposite is possible.

If they're saying "it must be true that P is used at most twice", then I have to test to see if "using P three times" is possible.

If they're saying "it must be true that F is 5th", then I have to test to see if it's possible for "F to NOT be 5th".

Since Q13 is asking whether we "must select at least one", we have to test whether "not selecting both" is possible.

So for each answer choice, you ask yourself, "could both of these letters be in the OUT column?" If so, eliminate the answer. If not, if they couldn't BOTH be out, then at least one of them must be in.

This is why your method for using Q12 for Q13 wouldn't really allow you to get rid of B/C/E.

Again, since Q12 said that a possible IN column is:
F, O, P, T, W
then a possible OUT column is:
G, N, V

If any of the choices for Q13 listed two letters from our possible OUT column, then we could get rid of that choice.

For example, if hypothetical answer (F) was
(F) G, V

We could eliminate it. We'd think, "I don't HAVE to put at least one of G and V in the IN column. I've already seen a possible scenario in Q12 in which both G and V were OUT."

(You could eliminate B/C/E from Q13 if the question read "which is a pair of foods BOTH of which must be in")

====
Alright, now for the deduction that speeds things up for Q13.

In Grouping games, we rarely create Frames, but occasionally we'll get "Chunks", which often lend themselves to Frames.

In this game, the 3rd rule is a "Chunk" rule. It essentially tells us that P and W are both IN or both OUT.

frame 1
IN: P W _ _ _ OUT: _ _ _
frame 2
IN: _ _ _ _ _ OUT: P W _

(the more interesting frame is frame 2, because the PW chunk has almost filled up the OUT column).

The 5th rule tells us that N and V cannot both be in. If N is IN, then V is OUT. If V is IN, then N is OUT.

Since they can't both be IN, we know at least one of them is OUT.

Let's add a placeholder to our OUT column, giving us this:

frame 1
IN: P W __ __ __ | OUT: N/V __ __
frame 2
IN: __ __ __ __ __ | OUT: P W N/V

You may notice that our OUT column is now full in frame 2. That means that everyone else has to be IN. Start with the other half of that N/V placeholder: put a V/N into the IN column. Then just fill in everyone else and make sure it doesn't break any rules.

frame 2
IN: F G O T V/N | OUT: P W N/V

We got our dess/main/side. We got out hot food. We're not breaking any rules. Good to go.

So you end up going into this game with these two frames:

frame 1
IN: P W __ __ __ | OUT: N/V __ __

frame 2
IN: F G O T V/N | OUT: P W N/V

Now when we look at Q13, we're asking ourselves, for each answer choice, "Is it possible for both these letters to be OUT?"

(A) there's room in frame 1 for F and T to be OUT
(B) there's room in frame 1 for G and O to be OUT
(C) there's room in frame 1 for N and T to be OUT
(D) P is only OUT in frame 2, and there's no room for O.
(E) there's room in frame 2 for V and W to be OUT.

Hope this helps. Let me know if you found any of it confusing.

[velvet]

Definitely makes sense. Just want to make sure this idea of mutually exclusive pairs (i.e. N/V) is exclusive to closed binary games, and has no bearing on open games, correct? I don't think too many of the worked out solutions usually notate this inference on the "Out" side; is it a good idea to always notate it in closed binary games just so one doesn't forget about it? It seems pretty useful.

Thanks in advance.

[rinagoldfield]

13.
(D) is correct.
Another way of phrasing this question is to ask "which one of the following pairs CANNOT be out at the same time?" This question is best approached by going through the answer choices one at a time and seeing if any constraints are broken by placing both letters in the "out" column. Only answer choice (D) does this_ if O and P are both out, then G and W are also both out. This leaves us with four letters immediately out_ one more than the three required. (D) is the correct answer.