Setup and Rule Diagrams

[Mariam]

hello- I understand why the T/J inferences are correct. I just don't really know how to get there. I did the game without it and I feel like it took longer than it should have. I am not sure that I would see this inference or look for it if I did the game, or a similar game, over. What should I be looking for?

I hope that makes sense. Thanks!

[KG!]

Hi KG!

Certain inferences, like the inferences you mention about the positioning of T and J, are helpful when it comes to answering questions, but perhaps not necessary to see right off the bat when you're diagramming a scenario. I'd put these T/J inferences in that category for sure. As long as you saw them once you started diagramming in response to a local question, you're still in position to complete the game efficiently and accurately.

But if you spend a little time after the fact thinking about the inferences, you'll see they weren't overly difficult to arrive at even during the setup. First, J's being mentioned in two different rules leads me to think about J being a fairly limited variable. It only has 4 spaces it can occupy anyway because of the "not 1 or 6" rule. And J is further controlled by T. So think for a moment about where J will have to go if T is placed in certain positions:

With T in 2, J cannot be in 3 (next to it), so J would have to be 4 or 5.

With T in 3, J cannot be in 2 or 4 (next to it), so J would have to be 5 (there's your T3 J5 inference!).

With T in 4, J cannot be in 3 or 5 (next to it), so J would have to be 2 (there's your T4 J2 inference!).

With T in 5, J cannot be in 4 (next to it), so J would have to be 2 or 3.

Worth it to cycle through all those options before looking at questions? Maybe, if you can cycle through them very quickly. Otherwise, let the inference arise organically as you approach the local questions (and you'll likely not find yourself in any major difficulty from a timing or accuracy perspective).

I hope this helps!

Jeremy

I see now! thanks for the explanation!!!

[Paul Marsh]

Hi Mariam! Great question. Whenever an inference doesn't pop out at you, it's always worth examining how you can get that inference faster next time. Here, it's just a matter of experience. You can practice forming these kinds of inferences and you'll be able to spot them quicker. There are two basic areas that you can work on to improve at forming these sorts of inferences:

1) Look hard at any variable that pops up in more than one rule. Here, J appears in two rules (Rules 4 and 5, well and Rule 1 but that's not as helpful). Whenever a variable is in two rules like this, it's very likely that we can find a way to combine those two rules into some sort of inference (even if it's just a small one). Take a minute to explore all the possibilities involving that variable to see if some sort of inference can be made.

2) When you're practicing Logic Games without a timer, I strongly encourage you to make the effort on your initial diagram to go through and think about as many possibilities as you can of where every variable can go and how it's affected by other rules. When you're practicing like that, don't think "how can I solve this game quickly", but think about how you can explore all the options of the game. So for this game, you'd go through and think about as many scenarios as you could, like, "Ok, so J can go 2 3 4 or 5. What if J goes 2 and K goes 3? That means H can't go 1 because of Rule 1, S can't go 1 because of Rule 3, and T can't go 1 because of Rule 5. That means R would have to go 1." And just play around with all of the possibilities in your master diagram before moving onto any of the questions. You won't do this on a timed test of course, and even doing it for every practice question is excessive, but at least occasionally give it a try. It's time consuming but it forces you to really think through every aspect of a game. The more you do this, the more you'll be able to quickly "see" how a variable's possibilities are limited without having to draw them all out.

Hope that helps!

[Mariam]

Yes- very helpful. Thanks!!

[spitzerh]

For the inference T2 --> J4 and T3-->J5, since T affects J more because it cannot be in 1st or 6th place, is the CP still applicable here? 

Thank you for your help!

[Adam Tyson]

You have one of those inferences reversed, spitzerh, and I presume that is a typo. If T is 2, J can be 4 or 5. The correct inference is if T is 4, J must be 2 (because it cannot be 1, 3, 5, or 6 in that case). And yes, the contrapositive does work in both cases! If J is not 2, then T cannot be 4, and if J is not 5, T cannot be 3! The inferences and contrapositives are as follows:

T4 J2
J2 T4

T3 J5
J5 T3

Be careful not to make a Mistaken Reversal, though! If J is in the 2nd position, T does not need to be 4th, because it could also go 5th or 6th. Likewise, if J is in the 5th position, T doesn't have to go 3rd because it could also go 1st or 2nd.

[Window]

I’m sorry but one thing eludes me in this logic game: why can’t T be in 1 or 6?

I must be missing something, otherwise if T is in 1, then J could be in 2, 3, 4, or 5 and similarly if T is in 6 then J could still be in 2, 3, 4, or 5? I came up with an example which conforms to all rules assuming T can be in 1 or 6 (TRJHSK), so I felt I was making unnecessary assumptions if I added to the general setup that T cannot be in 1 or 6.

Was this a mistake, refraining from adding it to my general setup? And if so what logical step am I overlooking which allows me to remove the possibilities of T in spots 1 and 6? I’ve been mulling this over for so long I don’t know if I even trust any answer my brain provides. TIA

[Window]

Apologies, one correction to my statement: if T is in 1 then J could be in 3, 4, or 5 due to Rule 5 and if T is in 6 then J could be in 2, 3, or 4 due to Rule 5. While I can recognize Rule 5 prohibits T from 1 if J is in 2 and prohibits T from 6 if J is in 5, those are under specific conditions/setups and therefore I opted to keep them to a specific scenario sketch rather than assume it would work with all scenarios as in the general setup. Am I missing anything aside from the above correction/specification?

[srusty]

Apologies, one correction to my statement: if T is in 1 then J could be in 3, 4, or 5 due to Rule 5 and if T is in 6 then J could be in 2, 3, or 4 due to Rule 5. While I can recognize Rule 5 prohibits T from 1 if J is in 2 and prohibits T from 6 if J is in 5, those are under specific conditions/setups and therefore I opted to keep them to a specific scenario sketch rather than assume it would work with all scenarios as in the general setup. Am I missing anything aside from the above correction/specification?

Hi,

No - you're in the right spot! We can't rule from our intial deductions that T cannot be in space 1 or 6. Because, like you say, those are very local or specific scenarios, we don't need to add it to our general sketch.

Hope this helps!