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- Thu Aug 31, 2017 6:40 pm
#39061
Setup and Rule Diagram Explanation
This is an Advanced Linear: Balanced game.
The game scenario establishes that each of four historians must give a lecture on one of four different topics. Essentially, we need to determine the order of two sets of variables:
This creates an Advanced Linear diagram, and because there are eight variables for the eight positions, this is a Balanced game. With the basic structure in place, let us now turn to the rules.
The first rule establishes that O and W must both be earlier than L:
This rule creates the following four Not Laws:
The second rule establishes that F must be earlier than O. Since F and O belong to two separate variable sets, it is best to represent the rule in a way that takes into account the stacked nature of the sets in our diagram:
This rule creates the following three Not Laws:
Notice that the first and the second rules both restrict the placement of O. When combined, these two rules produce the following sequencing chain:
The third rule establishes that H must be earlier than both G and J:
This rule adds a few more Not Laws to our diagram:
With only four variables per set, there are enough restrictions to create multiple dual options within the base setup:
You should also notice that since F and H cannot be the last two historians who deliver their lectures, they must then be the first two historians who deliver their lectures,. Consequently, neither one of them can give the L lecture:
Thus, we arrive at the final setup for this game:
With as many as six dual options in a game of eight variables, this setup is heavily restricted. A templates-based approach is not out of the question, especially if you noticed that the historians are the more heavily restricted variable set. In the interests of full coverage, let’s take a moment to explore what a Templates approach would look like. This approach isn’t necessary to conquer this game, but the level of restriction causes some students to explore it, which isn’t at all unreasonable. Essentially, this game is a good example of where using Templates is a decision driven by personal preference.
Of particular importance to this approach is F, because—thanks to the second rule—F is the only historian whose placement would have any effect in restricting both variable sets simultaneously. So, an excellent way to create templates would be to use the order in which the historians deliver the four lectures, with F as the driving force behind that approach. We can safely disregard the relative placement of G and J, because neither of them has any effect on the order of the other six variables.
You may notice that one of the variable sets in Template 1 remains relatively undefined. In particular, it does not capture the implications of the first rule on the order in which the topics are delivered. To take that rule into account, you could choose to “split” Template 1 into two:
With these three templates in place, attacking the questions would be relatively straightforward.
This is an Advanced Linear: Balanced game.
The game scenario establishes that each of four historians must give a lecture on one of four different topics. Essentially, we need to determine the order of two sets of variables:
This creates an Advanced Linear diagram, and because there are eight variables for the eight positions, this is a Balanced game. With the basic structure in place, let us now turn to the rules.
The first rule establishes that O and W must both be earlier than L:
This rule creates the following four Not Laws:
The second rule establishes that F must be earlier than O. Since F and O belong to two separate variable sets, it is best to represent the rule in a way that takes into account the stacked nature of the sets in our diagram:
This rule creates the following three Not Laws:
Notice that the first and the second rules both restrict the placement of O. When combined, these two rules produce the following sequencing chain:
The third rule establishes that H must be earlier than both G and J:
This rule adds a few more Not Laws to our diagram:
With only four variables per set, there are enough restrictions to create multiple dual options within the base setup:
You should also notice that since F and H cannot be the last two historians who deliver their lectures, they must then be the first two historians who deliver their lectures,. Consequently, neither one of them can give the L lecture:
Thus, we arrive at the final setup for this game:
With as many as six dual options in a game of eight variables, this setup is heavily restricted. A templates-based approach is not out of the question, especially if you noticed that the historians are the more heavily restricted variable set. In the interests of full coverage, let’s take a moment to explore what a Templates approach would look like. This approach isn’t necessary to conquer this game, but the level of restriction causes some students to explore it, which isn’t at all unreasonable. Essentially, this game is a good example of where using Templates is a decision driven by personal preference.
Of particular importance to this approach is F, because—thanks to the second rule—F is the only historian whose placement would have any effect in restricting both variable sets simultaneously. So, an excellent way to create templates would be to use the order in which the historians deliver the four lectures, with F as the driving force behind that approach. We can safely disregard the relative placement of G and J, because neither of them has any effect on the order of the other six variables.
You may notice that one of the variable sets in Template 1 remains relatively undefined. In particular, it does not capture the implications of the first rule on the order in which the topics are delivered. To take that rule into account, you could choose to “split” Template 1 into two:
With these three templates in place, attacking the questions would be relatively straightforward.
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