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- Sat Oct 19, 2013 11:00 pm
#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:
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:
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:
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:
This relationship can also be represented on the diagram via Not Laws underneath the base:
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:
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:
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:
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:
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:
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:
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:
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:
This relationship can also be represented on the diagram via Not Laws underneath the base:
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:
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:
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:
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:
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