Setup and Rule Diagrams

[Administrator]

Please post your questions below!

[ava17]

Hi,

For the second rule for this question, how do we know whether it is Q --> QG or G --> GQ?

Thanks!

[Adam Tyson]

Thanks for the question, ava17! The key there lies in the previous rule, in my opinion - there is only one G in the game. If that's the case, then combining that info with the rule you are asking about, we can be sure that wherever that one G sits in the order, there is a Q right before it, but we cannot be assured that every Q has a G right after it because there might be two Qs in the game. Something has to go twice, right? If there could be two Qs, then there is no way that they could each be followed immediately by a G, because then there would be two Gs as well. So, just given the numbers, a rule of Q QG simply doesn't make sense. Instead, the one G we have must be the sufficient condition: G QG. In other words, wherever our lone G goes, a Q goes to the left of it.

Combine rules to make powerful inferences!

[menkenj]

For this game, I used two worlds as my set up. Since there is only one G in the game and Q must come before G, yet Q cannot come on Friday, then this means there are only two scenarios. QG on M/T or QG on T/W.

[Adam Tyson]

That makes sense, menkenj, as there is nowhere else for that QG block to go, but then what? Neither of those templates really goes anywhere after that. Which variable is used twice - Q, P, or L? And where do you put N? Templates are great when they take you somewhere further than just the split between the two options you are exploring, but may not be very helpful otherwise.

Then again, drawing out these two templates should take very little time, and you should quickly see that they give you no additional inferences, so you can just stop right there and refer to them as you answer local questions to see if they provide any help. Not a huge help, but also not a real hindrance or time waster, so what the heck, why not?

[menkenj]

That makes sense, menkenj, as there is nowhere else for that QG block to go, but then what? Neither of those templates really goes anywhere after that. Which variable is used twice - Q, P, or L? And where do you put N? Templates are great when they take you somewhere further than just the split between the two options you are exploring, but may not be very helpful otherwise.

Then again, drawing out these two templates should take very little time, and you should quickly see that they give you no additional inferences, so you can just stop right there and refer to them as you answer local questions to see if they provide any help. Not a huge help, but also not a real hindrance or time waster, so what the heck, why not?

Indeed. For this game, having the bare templates was useful to get me started and put my mind at ease. I can free myself from thinking about one of the rules and internalize the others.

[hope]

Could an administrator provide the diagram with the rules. Thank you.

[kupwarriors9]

Could an administrator provide the diagram with the rules. Thank you.

Hi Hope!
This is my take on it.

GLNPQ5, where N = once, G = once (Therefore, either L and P can be twice. Q can't be twice because it has to always be in front of G and G can only be used once).

[ADMIN NOTE: While most of this student-provided diagram is great, the above inference about Q is incorrect. See the discussion earlier in this thread about the proper interpretation of the QG rule. G can only go once, but Q could go twice, one time followed by G and another time not followed by G.]

IQGI
(I couldn't do the proper powerscore notation here. Sometimes I write it like Q# G#+1 (can you tell I'm a stem major from that notation??? Haha)

However, since Q cannot be on Friday, that means G can never be on saturday or friday!!!

P = always thursday (as per rule 5).
P = saturday.

*** Thus, P can only be Monday and Thursday or just Thursday as it cannot be on consecutive days, ruling out Friday and Wednesday.

Combining the two inferences above, lets us understand that Q can only work on Monday or Tuesday, and G can only work on Tuesday (when Q= Monday) and Wednesday (when Q=Tuesday). Thus, either Q or G is only ever on Tuesday.

Now to figure out N and L, we have to consider if P or L is twice.
When P is twice:
Pm Qtu Gw Pth N/Lf L/Ns

** Note:N or L can only either be on Fri or Saturday.

When L is twice, there is more than one hypothetical we can make:
Qm Gtu Lw Pth N/Lf L/Ns

Lm Qtu Gw Pth N/Lf L/Ns


Also one thing to note is N can only be on friday or saturday because it can only be used once (rule 1 & 2) and since the items used twice can not appear consecutive.


HOPE THIS HELPS

[hope]

Yes, your diagram and explanation of rules helped quite a bit. In fact, you made it seem so easy. Thanks a bunch!

[Rachael Wilkenfeld]

Awesome work, kup!


The only thing I would change in your diagram is that I'd make it more clear that F and S need exactly one N and one L.

I would draw it something like this:

Pm Qtu Gw Pth (N, L)

Where the N, L go on top of the long lines. That shows that you couldn't pick 2 Ls or 2 Ns for those slots.

Great work again!