- Sun Jan 20, 2013 12:00 am
#25621
Setup and Rule Diagram Explanation
This is a Linear/Grouping Combination game.
The game scenario establishes that each of three films (G, H, and L) is shown at least once during a film festival held on Thursday, Friday, and Saturday:
Because of the order inherent to the three weekdays, it is best to use them as our base. As suggested in the scenario, more than one film can be shown on any particular day, but no film can be shown more than once on a given day. Thus, the maximum number of films that can be shown on any given day is 3. However, it is always advantageous to read through the rule set before deciding on a particular setup. Apparently, if more than one film is to be shown on a given day, the order of these films matters as well, as suggested by the warning at the end of each rule (“…and no film is shown after it on that day,” emphasis added). To represent this, we can take advantage of the vertical axis in our setup: since the films shown on a given day form a vertical group, we can decide to place the last film to be shown that day at the bottom of our vertical group:
Why focus on the last film, and not the first? Because the rules suggest that we should: each rule indicates which film is to be shown last on a given day. Representing this type of information will be made significantly easier if we can label as “last” the film being referenced in each rule. Of course, there is always the possibility that only one film is being shown on a given day, in which case this signification would be irrelevant. We can simply place the solitary film in a “box” to designate the defined nature of that group.
It is also important to acknowledge another level of complexity here: we know neither the number of times each film is shown during the festival, nor the number of films shown on each day. In other words, neither the size of the variable set, not the size of each group, is fully defined. Consequently, creating an exhaustive list of every possible Fixed distribution in this game would be counterproductive. However, you should at least analyze the minimum and the maximum number of films that can be shown on each day. Uncertainty in group sizes is never a good thing, which is why you need to attempt to confine it as much as possible. Examining the min/max limits of each group would be a good place to start.
The first rule states that H is shown on Thursday, warning us that no film is shown after it on that day:
To be clear, it is entirely possible that other films are shown before H on Thursday. The minimum and the maximum number of films shown on that day is therefore one and three, respectively:
The second rule stipulates that either G or L, but not both, is shown on Friday, and no other film is shown after it on that day:
Take a moment to understand this rule well: simply placing a G/L dual-option on Friday is not enough. Since no other film can be shown after G or L on Friday, we need to make sure that the dual-option is clearly marked as “last.” Furthermore, we are prohibited from showing both G and L on Friday, suggesting that the maximum number of films to be shown on that day is two:
The third rule uses language identical to that in second rule: either G or H, but not both, is shown on Saturday, and no other film is shown after it on that day. This generates a G/H dual-option on Saturday, and also limits the maximum number of films to be shown on that day to two:
The numerical restrictions resulting from the last two rules suggest that the total number of film showings during the festival is 7.
Game setups seek to capture absolutes: what must be true, and what cannot be true. We need not indicate, for instance, the fact that H could be shown before G or L on Friday, or that L could be shown before G or H on Saturday. Indeed, there are few inferences in this game, as neither the variable set, nor the three groups, are sufficiently restricted. Due to the complex nature of the rules, however, you can expect that the questions will test your understanding of them directly.
The final diagram for the game should look like this:
This is a Linear/Grouping Combination game.
The game scenario establishes that each of three films (G, H, and L) is shown at least once during a film festival held on Thursday, Friday, and Saturday:
Because of the order inherent to the three weekdays, it is best to use them as our base. As suggested in the scenario, more than one film can be shown on any particular day, but no film can be shown more than once on a given day. Thus, the maximum number of films that can be shown on any given day is 3. However, it is always advantageous to read through the rule set before deciding on a particular setup. Apparently, if more than one film is to be shown on a given day, the order of these films matters as well, as suggested by the warning at the end of each rule (“…and no film is shown after it on that day,” emphasis added). To represent this, we can take advantage of the vertical axis in our setup: since the films shown on a given day form a vertical group, we can decide to place the last film to be shown that day at the bottom of our vertical group:
Why focus on the last film, and not the first? Because the rules suggest that we should: each rule indicates which film is to be shown last on a given day. Representing this type of information will be made significantly easier if we can label as “last” the film being referenced in each rule. Of course, there is always the possibility that only one film is being shown on a given day, in which case this signification would be irrelevant. We can simply place the solitary film in a “box” to designate the defined nature of that group.
It is also important to acknowledge another level of complexity here: we know neither the number of times each film is shown during the festival, nor the number of films shown on each day. In other words, neither the size of the variable set, not the size of each group, is fully defined. Consequently, creating an exhaustive list of every possible Fixed distribution in this game would be counterproductive. However, you should at least analyze the minimum and the maximum number of films that can be shown on each day. Uncertainty in group sizes is never a good thing, which is why you need to attempt to confine it as much as possible. Examining the min/max limits of each group would be a good place to start.
The first rule states that H is shown on Thursday, warning us that no film is shown after it on that day:
To be clear, it is entirely possible that other films are shown before H on Thursday. The minimum and the maximum number of films shown on that day is therefore one and three, respectively:
The second rule stipulates that either G or L, but not both, is shown on Friday, and no other film is shown after it on that day:
Take a moment to understand this rule well: simply placing a G/L dual-option on Friday is not enough. Since no other film can be shown after G or L on Friday, we need to make sure that the dual-option is clearly marked as “last.” Furthermore, we are prohibited from showing both G and L on Friday, suggesting that the maximum number of films to be shown on that day is two:
The third rule uses language identical to that in second rule: either G or H, but not both, is shown on Saturday, and no other film is shown after it on that day. This generates a G/H dual-option on Saturday, and also limits the maximum number of films to be shown on that day to two:
The numerical restrictions resulting from the last two rules suggest that the total number of film showings during the festival is 7.
Game setups seek to capture absolutes: what must be true, and what cannot be true. We need not indicate, for instance, the fact that H could be shown before G or L on Friday, or that L could be shown before G or H on Saturday. Indeed, there are few inferences in this game, as neither the variable set, nor the three groups, are sufficiently restricted. Due to the complex nature of the rules, however, you can expect that the questions will test your understanding of them directly.
The final diagram for the game should look like this:
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