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#40573
Setup and Rule Diagram Explanaton

This is an Advanced Linear: Balanced game.

The game scenario establishes that five movies are being shown at a theater during the course of a single evening. The five movies are each shown once, on one of three separate screens—screens 1, 2, and 3. Next, the test makers specify a tricky lineup of movie show times: screens 1 and 2 show two movies, each at 7 and 9, and screen 3 shows one move at 8. This is clearly a Linear element. How you use this element to set the game up then has a significant impact on how difficult you find this game.

There are several possible angles from which to set up this game, and they all revolve around choosing a base for the game. The first base that could be used is all five movie times, which would create a linear base of 7-7-8-9-9 (the movie screens are then another row above the times, filled in with the screen number 1-2-3-1-2). However, this approach is inefficient because the repetition of the 7s and 9s would increase the likelihood of error (in a typical setup you want to avoid repeating any base element if at all possible).

The second base that can be used is the grouping aspect of the three screens. This has promise, but it depends on how the movie times are then shown. If the movie times are represented as two spaces above screens 1 and 2, and one space above screen 3, the result is the following diagram:
PT70 -Game_#3_setup_diagram 1.png
PT70 -Game_#3_setup_diagram 1.png (2.01 KiB) Viewed 1475 times
This setup is problematic because it does not sufficiently capture the Linear aspect of the movie times, and test takers will have to slow down to determine the relationship between times.

The last approach is the best because it combines elements of both approaches above. First, a linear base of the movie times is used, with each time shown just once (7-8-9). Next, the movie screens are stacked above the base, with one row for each screen, creating an Advanced Linear setup:
PT70 -Game_#3_setup_diagram 2.png
PT70 -Game_#3_setup_diagram 2.png (2.76 KiB) Viewed 1475 times
This setup capture both the screens as well as the linear aspect of the times. However, because there are only five movies, only five of these slots are available, and four of the screen/time slots must be eliminated. This can be done by placing either an E (for “empty”) or X variable (which we will use) over those slots to indicate that they are unavailable, leading to the initial setup from just the game scenario:
PT70 -Game_#3_setup_diagram 3.png
PT70 -Game_#3_setup_diagram 3.png (5.42 KiB) Viewed 1472 times
With this setup in place, let’s examine each of the rules.

The first rule is sequential, and establishes that W begins before H begins:
PT70 -Game_#3_setup_diagram 4.png
PT70 -Game_#3_setup_diagram 4.png (922 Bytes) Viewed 1475 times
This relationship can also be represented on the diagram via Not Laws underneath the base:
PT70 -Game_#3_setup_diagram 5.png
PT70 -Game_#3_setup_diagram 5.png (5.39 KiB) Viewed 1475 times
Because there are only three separate movie show times, if one of W or H is shown at 8 P.M., then the show time of the other movie is known (but not the screen). Specifically, if W is shown at 8, then H must be shown at 9, and if H is shown at 8, then W must be shown at 7:
PT70 -Game_#3_setup_diagram 6.png
PT70 -Game_#3_setup_diagram 6.png (2.34 KiB) Viewed 1475 times
Writing these two inferences out is not necessary, but there is no harm in doing so.

The second and third rules are similar. The second rule eliminates S from being shown on screen 3, and the third rule eliminates R from being shown on screen 2. These should be shown on the diagram as Not Laws, but on the “side” of the diagram since the screen numbers are represented vertically. You can place them on either the left side or the right side of the diagram as you prefer. We will place ours on the left side next to the screen numbers (and thus closest to the screen number itself) since this game contains a lot of information:
PT70 -Game_#3_setup_diagram 7.png
PT70 -Game_#3_setup_diagram 7.png (5.59 KiB) Viewed 1475 times
Because there are only five movies being shown, eliminating just two movies from contention starts to restrict some of the movie show times on certain screens. For example, the 7 P.M. showing on screen 2 can only be M, S, or W (since H and R have been eliminated). Similarly, the 9 P.M. showing on screen 2 can only be H, M, or S, (since R and W have been eliminated). These could be shown as triple-options on each space, but only do so after considering the remaining rule, in case further restrictions are revealed.

The fourth rule establishes that H and M are shown on different screens. In the context of the setup above, if the two movies were shown on the same screen, that would be a horizontal block. Thus, if the two movies are not shown on the same screen that is a horizontal not-block, which rotates since the times of H and M are not fixed:
PT70 -Game_#3_setup_diagram 8.png
PT70 -Game_#3_setup_diagram 8.png (2.18 KiB) Viewed 1475 times
Operationally, no inference can be drawn from this rule until the variables are placed, but note that since H appears in both the first and fourth rules, there is a connection between the two that in solving some of the questions.

There are no randoms in the game, and by adding the triple-options mentioned earlier, we arrive at the final diagram:
PT70 -Game_#3_setup_diagram 9.png
PT70 -Game_#3_setup_diagram 9.png (11.7 KiB) Viewed 1475 times
 josheli
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#14410
I struggled with the setup of this game. I found it difficult to find those strong inferences and I ended up answering the majority of the questions by testing them out individually, which took a long time to do. May someone please help me with the setup of game and point out the key inferences?
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 KelseyWoods
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#14418
Hi Josheli!

This is an Advanced Linear game. You can use the screens (1, 2, 3) as your base and then stack the times (7, 8, 9) above them. Since screens 1 & 2 don't have showings at 8pm, you can X out those slots on your diagram. You can also X out the 7pm and 9pm slots on screen 3, since that screen only has one 8pm showing. This will give you 5 remaining slots for your 5 movies.

From the first rule, we can infer that the western cannot be shown at 9pm and the horror film cannot be shown at 7pm. To show this on your diagram, use Side Not Laws.

The second and third rules are fairly straightforward. Show them using Not Laws.

The final rule can be diagrammed with a couple of Not Blocks, showing that you can't have H above M or M above H.

There aren't a ton of complicated inferences here but it is important to make sure you have a clear diagram with a complete set of Not Laws.

As you're going through the questions, think about how the rules interact with one another and what happens to the other variables once you've placed some of them. The H/M rule ends up popping up a lot. Whenever you place some variables on your mini-diagrams, you need to make sure that you're not forcing H and M onto the same screen.

Hope this helps!

Best,
Kelsey
 mostofthetime
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  • Joined: Dec 09, 2020
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#82101
Hello Powerscore,

My question is just on this part of the explanation: "Because there are only three separate movie show times, if one of W or H is shown at 8 P.M., then the show time of the other movie is known (but not the screen). Specifically, if W is shown at 8, then H must be shown at 9, and if H is shown at 8, then W must be shown at 7:"

... I was just wondering if in the case of the horror film playing at 9, isn't it true the western could be shown either at 7 or at 8? And so it's not always true that knowing the time of one gives away the time of the other?

Maybe this is a minor point, but thought I should ask.

Thank you!
 Robert Carroll
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#82150
m,

Note the original post (which you also quoted):
if one of W or H is shown at 8 P.M., then the show time of the other movie is known
The post is not saying that knowing W or H will automatically tell you the time of the other one. It's saying that knowing that W or H is at 8 specifically will tell you the time of the other one.

Robert Carroll

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