Q6

[Richard.Arpin]

H, K, L, not necessarily in that order, give morning reports; what must be true?

I'm confused as how to make the deductions in this game, I think it has to do with how I'm interpreting the rule attaching N, H, and I.

My setup looks like this:
morn: _ _ _ with H, K, L
after: _ _ _ with G, I, N

I've eliminated O and R from the afternoon portion of the setup as they can only be in the morning. So I've got the six elements, but now ordering,

I get this far:
morn: _ _ _ with H,K, L
after: I G N

G is limited to Tuesday, and N cannot be Monday since that would create a scenario where the setup rule 3 would be broken. I don't see how the rule then forces I onto Monday and doesn't allow H for Monday though?

I interpret rule 3 as:
(If Nmon or Ntue --> H/I(I/H) next day) if not Nwed
or put into another form
If Nmon or Ntue --> H/I(I/H) next day
but that only gives us a sufficient statement about if we know where N is placed

What then is the contrapositive of the original unless (if not) rule?
if Nwed --> (Not Nmon or Not Ntue --> H/I(I/H) separate days
or is it:
if Nwed --> (Not Nmon or Not Ntue --> H/I(I/H) same day but not next day

How do we ascertain that Nwed is a trigger for I/H not to be on the same day?

Is a logic statement within another logic statement doubly negated when forming the contra positive or just one of the logic pieces?

Have I missed a step in this game because maybe I'm not even breaking down the bracketed necessary clause deep enough, I'm not really considering it's days jointly as one entity to be negated and it's relationship to N as another entity to be negated.

I guess what I'm saying is rule 3 has me confused because I have no idea how they get to Nwed --> I cannot be on same day as H

[Richard.Arpin]

Thinking about it a bit more could the rule be written:

If (neg)Nwed --> Nmon or Ntue --> H/I(I/H) together on day and day after N

But this then negated becomes

I or H separate or not together on a day following N --> Not Nmon or Ntue --> Nwed

But this still is a problem sufficiency about knowing something about I and H and not what can be determined by knowing that Nwed is a condition met

[timmydoeslsat]

I just did this game this morning and I wanted to address this question of how to interpret the third rule.

If N ---> HI next day (morning-afternoon sequence of these 2 does not matter)

This rule states that this is the case unless N is on Wednesday.

If this unless part was not present in the rule, you could validly deduce that N could not be on Wednesday, but the rule is an unless rule.

So really the rule is saying:

~ [N---> HI next day] ---> N is on Wednesday

Contrapositive of that is:

~ N on Wednesday ---> [N ---> HI next day]


So the question to ask yourself is, what do I know if I have N? Well, if N is on Monday or Tuesday, the HI block will follow the next day.

If N is on Wednesday, we have no rules governing that!

We can have H and I do whatever they want with N being on Wednesday.

[eht1991]

So, if you go to the "diagram" post for this discussion topic, you will see that Noah laid out the game a bit differently, and in my opinion, in a way that makes it easier to visualize the constraints.

Basically, instead of stacking the morning and afternoon slots, lay them side by side. This allows us to organize clues that apply to morning/afternoon slots alongside clues that apply to the days in a coherent way.

This diagram takes care of our first and second constraints. Since there are only three days, we can simplify the third constraint as two separate conditionals:

N Monday ---> H and I Tuesday
N Tuesday ---> H and I Wednesday

We also know the contrapositives. In plain English:

If either H or I (or both) does not go on Tuesday, then N cannot go on Monday. If either H or I (or both) does not go on Wednesday, then N cannot go on Tuesday.

So for this problem:

If H, K, and L fill all the morning slots, then we know that O and R are ruled out of the game, because the only time they can go is in the morning. Thus, we must fill in the remaining (afternoon) slots with G, I, and N. Where to place these?

Well, we know that G cannot go on Monday or Wednesday, so it must go on Tuesday. That leaves us with N, and I to place. From our third constraint, we know that if N goes on Monday, then H and I both go on Tuesday; however, since G is already placed on Tuesday afternoon, we know this could not happen. So N must go on Wednesday and I, in turn, must go on Monday. This is as far as the inference chain will take us.


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**SPOILER ALERT**
As it turns out, answer choice B is consistent with the above inferences, so we can circle that one and move on.
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Hope that helps!

-Ernest

[ohthatpatrick]

I guess what I'm saying is rule 3 has me confused because I have no idea how they get to Nwed --> I cannot be on same day as H

You may have just misspoke here, but you were making it seem like (A) is wrong because H can't be on Monday. However, (A) is just wrong because H doesn't have to be on Monday.

In terms of your broader question about the unless at the end of this rule, Timmy definitely symbolized it correctly. But you may agree that it's pretty hard to digest the correct symbolization of negating an entire if/then rule.

Conversationally, the unless essentially provides an exception to the rule. It's just saying "this rule normally applies, unless it's Wednesday, in which case, whatevs."

Let me try to give an example of another "weird unless clause" rule that you might want to symbolize:

If Bob is 3rd, then Mary is 5th, unless Paul is 1st.

We have this general rule "B3 --> M5", and then this exceptional case of when Paul is 1st.

We could symbolize the rule as:
~P1 --> [B3 --> M5]
~[B3 --> M5] --> P1

Or we could make the rule a little more conversational in its symbolism. Basically, the rule applies as long as Paul isn't 1st.

So we could just add that idea to our sufficient condition:

If Bob is 3rd, then Mary is 5th, unless Paul is 1st.
B3 and ~P1 --> M5
~M5 --> ~B3 or P1

So, applied to the rule in this game, we could also write rule 3 as:
(N gives a report) and ~(N Wed.) --> H/I the following day

Hope this helps.