Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Defined-Fixed, Unbalanced: Overloaded game.

This game was widely regarded as the most difficult game of the exam, and as one of the hardest games in recent years. This is definitely a difficult game, and the test makers repeatedly force students to Hurdle the Uncertainty, which is one of the more challenging principles that appears in Logic Games.

The initial scenario appears as follows:

Jun 09__M12_game#3_L11_explanations_game#3_setup_diagram_1.png

Of immediate interest is the fact that exactly five dinosaurs are displayed, and exactly two dinosaurs are not displayed. Thus, any time two dinosaurs are not on display, the other five automatically are on display.

The first rule helpfully establishes that exactly two of the toys are mauve:

Jun 09__M12_game#3_L11_explanations_game#3_setup_diagram_2.png

With exactly two mauve toys, the remaining toys must be green, red, or yellow.

The second rule includes S in the display, and stipulates that S is red;

Jun 09__M12_game#3_L11_explanations_game#3_setup_diagram_3.png

This is a powerful rule, and it reduces the remainder of the game into a 6-into-4 scenario.

The third and fourth rules are similar, and both are conditional:

Jun 09__M12_game#3_L11_explanations_game#3_setup_diagram_4.png

In both cases, if the dinosaur is included in the display, then it is a specific color (but do not reverse the rules. For example, if a dinosaur is green, it does not have to be I). These two rules can also be combined with the first rule to determine that neither I nor P can be one of the two mauve toys:

Jun 09__M12_game#3_L11_explanations_game#3_setup_diagram_5.png

Because S is already known to be red from the second rule, the pool of candidates for the two mauve dinosaurs is down to L, T, U, and V. This fact will become critical shortly.

The fifth rule further reduces the pool of available dinosaurs:

• V U

The sixth rule also creates further limitations:

Jun 09__M12_game#3_L11_explanations_game#3_setup_diagram_6.png

Given that only L, T, U, and V are available for the two mauve toy slots, and that the fifth and sixth rules both address members of this group, one should suspect that some powerful inferences can be made about the mauve dinosaurs.

Because both L and U cannot be mauve, the candidate pool for the two mauve dinosaurs appears as L/U, T, and V. Thus, if either T or V is removed, the other must be displayed, and then one of L and U must be displayed. For example, If V is removed from the display, then T and L/U must be the two mauve toys on display.

Of course, the fifth rule also has a similar restriction, because V and U cannot be displayed. So, if either V or U is displayed, the other is knocked out, and the remaining options are limited. For example, if U is included in the display, then V cannot be included in the display, forcing T to be mauve (L or U could still be the other mauve dinosaur).

The sixth rule produces another inference, namely that if I and P are both selected, L and U cannot both be selected (because then L and U would both have to be mauve, a violation). This inference can be diagrammed as:

Jun 09__M12_game#3_L11_explanations_game#3_setup_diagram_7.png

This final inference plays only a minor role in the game. The main key to the game is understanding that the two mauve dinosaurs must be selected from the pool of L/U, T, and V. Identify this limitation, and the game is manageable. Fail to identify it, and the game seems nightmarishly difficult.

With the prior information, and the additional note that T is a random, we arrive at the final setup to the game:

PT57-Jun2009_LGE-G3_srd1.png

Note: Additional Not Laws, such as no further mauve toys can be displayed, could be shown, but seem unnecessary given the focus on that rule.

[stsai]

Q12-17. 7 toy dinosaurs in 4 colors, select exactly 5

I find this really hard even though it's only a basic linear game!
The only things in my setup are the basic rules:
D: S __ __ __ __
C: R M M __ __
I--> [IG] vertical block
P--> [PY]
V <--/--> U
L+U-->at least 1 Not M

This setup only got me to Q12, and I felt stuck from Q13 on...
Can someone please show the complete setup for this question?
Thanks!

[Dave Killoran]

Hi Stsai,

Let me make a couple of points about this game. first, it's not an easy game at all. Last November I wrote up a list of the 10 Hardest Logic Games of All Time ( http://blog.powerscore.com/lsat/killer- ... -all-time/ ), and this game made the list. So, the difficulty you ran into wasn't because of some issue on your part, but rather because this game is tough. In that same vein, I also included this game in our Advanced Logic Games http://www.powerscore.com/lsat/advanced ... _index.cfm course because while tough, it is solvable.

Second, this isn't a Linear game, but is instead a Grouping game. And it's the Grouping interactions that are really key to how this game operates.

Ok, that said, let's look at your setup. Your setup shows the basic rules, but misses the most powerful aspect of the game: the possibilities for the Mauve dinosaurs. We know that two mauve toys are included. Which dinosaurs can they be? Not S, because S is red. Not I and P, because they are green and yellow, respectively. So, the two mauve toys can only come from the group of L, U, T, and V. But wait, we can go even farther. The last rule means that L and U both cannot be mauve, reducing the possible candidates to L/U, T, V. And, the second-to-last rule eliminates the pairing of V and U. This means that there aren't that many options for the mauve dinosaurs, and identifying this limitation is one of the keys to the game. Let's look at #13 and see how it works:

Question #13: The question stem eliminates T from the display. That leaves the choices of L/U and V for the mauve dinosaurs. But, when V is selected, then U cannot be, and so the two mauve dinosaurs are V and L:

D: S V L __ __
C: R M M __ __

At this point, you know that D cannot occur and must therefore be the correct answer, but for demonstration purposes, let's finish off the setup.

With T and V now eliminated from the display, the final two dinosaurs must be I and P, and from the third and fourth rules we know their colors:

D: S V L I P
C: R M M G Y


Try the rest of the game with the ideas above in mind, and let's see how it goes. If you have any other problems, post back and I'll answer those questions.

Thanks!

[stsai]

That was really helpful! Recognizing the limited possibilities for the 2 M's helped me get through the rest of the questions. And it definitely made me feel better that this is among the top ten toughest games ever

By the way, I mismatched this game to the game type index in the back of the bible to be 2008, so I just changed the titles of my posts into 2009.

Thanks again, Dave!

[Dave Killoran]

Awesome, that's great to hear the game went better for you!

Thanks!

[nicolle828]

I just watched Dave Killoran's virtual video of the dreaded dinosaur game and have a question about his set-up. The rule I am referring to is the final rule where it is stated if two of the dinosaurs are included only one can be mauve. He diagrammed that rule, but my question is about his decision to then put it in the global set up. It says "if" they are both included so I didn't put them in my global set up because what if they aren't included? In his video, after putting them in the global, he talks at length about the different things that you can infer from being able to place them there, but I was concerned because of the "if". I know his placement end up being correct as he knows the rest of the game and all of the answers, but can I feel confident enough when there is an "if" to place something in my global set up diagram?

[Dave Killoran]

Hi Nicolle,

Thanks for the question! What I did there was I diagrammed inferences that followed from that rule and the other rules, not actually the rule itself. This is why the "if" still allows us to draw absolute conclusions about what could occur. Let's walk through it and see how that works

We know from the first rule that exactly two Mauve toys are included, and so we have reserved two space son our diagram for M. The second, third, and fourth rules then tell us that the Stegosaur (S), Iguanadon (I), and Plateosaur (P) are all colors other than mauve. Since there are only seven dinosaurs to begin with, removing those three means that only L, T, U, and V are available for the two mauve toy slots. Because the fifth and sixth rules both address members of this L, T, U, and V group, one should suspect that some powerful inferences can be made about the mauve dinosaurs.

The last rule tells us that both L and U cannot be mauve, and thus the candidate pool for the two mauve dinosaurs is actually L/U, T, and V (with L/U designating that at most one of L and U can be selected). That's what you see me diagramming there—the candidate pool available for the two mauve spaces (it's not stating that both L and U are being used). So, it's not the exact rule itself, but a consequence of all the rules with that one.

Please let me know if that helps. Thanks!

[nicolle828]

Dave,

My issue is still the "if" in the final rule and then putting it in the diagram.....what if they aren't both included as is necessary for that rule? Then aren't they mistakenly in the diagram? I have no issues with the rules or how to write them.....I just am concerned about including a rule that begins with "if" in my main diagram? Can I make that inference safely?

Couldn't it be T and V are mauve and then the other two use the rules about the Y and G and so the I and P are the final dinosaurs?

Thank you for answering so quickly!!

Nicolle

[Dave Killoran]

HI Nicolle,

Thanks for the reply! What's happened is that the "ifs" in the game have actually allowed us to make global inferences about possible outcomes, and, actually, this is just one of many instances in games where an "if" results in a concrete truth.

If you think about it, "if" statements fundamentally deal with possibilities ("If this occurs, then..."), and there are many times in our diagrams that we try to show the range of possible outcomes. For example, let's start with a simple Grouping game where 8 students are being divided into two groups of 4. If we have a rule that says, "If A is selected, then B cannot be selected," then we'd get the following notation on the diagram:

• __ __
  __ __
  __ __
  A/B B/A
  1 2

So, even though we had an "if" in play, it still allowed us to draw a solid conclusion about what is possible within the game (that namely there are two possible outcomes: A in the first group and B in the second group, or B in the first group and A in the second group).

That's very similar to what is occurring in the dinosaur game. What that representation of "L/U, T, V" in a box means is that the two spaces will be filled from the range of L/U, T, or V. So, it's entirely possible that T and V get selected (just as it could be L and T, or L and V, etc). I think what's bothering you is that it looks like L/U is "in" the game, but you have to instead look at the notation—it just represents a range of what is possible. Just like the A/B notation in my first example doesn't mean that both are there, the "L/U, T, V" notation transmits two pieces of data: 1. that L and U can't both be there (from the L/U notation), and 2. that two from the group of L/U, T, and V will be selected (from the L/U, T, V notation).

Please let me know if that helps. Thanks!

[nicolle828]

Dave,

Wow!! A lightbulb just went off!!! A true ah-ha moment! You are showing what could happen: L/U, T, V!! I am so grateful for all of your help!! Thank you!

Nicolle