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#25104
Setup and Rule Diagram Explanation
This is a Grouping/Linear Combination: Numerical Distribution, Identify the Templates game.
The game scenario indicates that eight books are placed on three shelves, with at least two books per shelf (which establishes a minimum distribution of 2-2-2). The first rule then states that more books are placed on the bottom shelf than on the top shelf. This creates two Numerical Distributions:
The presence of these two distributions immediately suggests that the game should be approached with templates.
The second rule places I on the middle shelf, and the remaining three rules create a FM block and two sequencing rules. These rules create the following initial, basic setup:
Let us now examine the templates. There will be three templates—one for each of the distributions, but then the 2-3-3 template will be split into two templates based on the position of the FM block.
Template #1: 2-3-3 Distribution, FM Block on Middle Shelf
In this template, the FM block is placed on the middle shelf, which then forces K onto the top shelf per the third rule. With the middle shelf “full,” O must go on the top shelf, leaving L on the bottom shelf, along with G and H:
Template #2: 2-3-3 Distribution, FM Block on Bottom Shelf
In this template, the FM block is placed on the bottom shelf, which opens the scenario up considerably. A number of possible solutions fit under this template, but because of the Not Laws, you can deduce that one of G, H, and L is placed on the bottom shelf:
Template #3: 2-2-4 Distribution
In this template, the FM block must be placed on the bottom shelf, which again opens the scenario up considerably. A number of possible solutions fit under this template, but because of the Not Laws, you can deduce that exactly two of G, H, and L are placed on the bottom shelf:
With the three templates in place, we are ready to attack the questions.
This is a Grouping/Linear Combination: Numerical Distribution, Identify the Templates game.
The game scenario indicates that eight books are placed on three shelves, with at least two books per shelf (which establishes a minimum distribution of 2-2-2). The first rule then states that more books are placed on the bottom shelf than on the top shelf. This creates two Numerical Distributions:
The presence of these two distributions immediately suggests that the game should be approached with templates.
The second rule places I on the middle shelf, and the remaining three rules create a FM block and two sequencing rules. These rules create the following initial, basic setup:
Let us now examine the templates. There will be three templates—one for each of the distributions, but then the 2-3-3 template will be split into two templates based on the position of the FM block.
Template #1: 2-3-3 Distribution, FM Block on Middle Shelf
In this template, the FM block is placed on the middle shelf, which then forces K onto the top shelf per the third rule. With the middle shelf “full,” O must go on the top shelf, leaving L on the bottom shelf, along with G and H:
Template #2: 2-3-3 Distribution, FM Block on Bottom Shelf
In this template, the FM block is placed on the bottom shelf, which opens the scenario up considerably. A number of possible solutions fit under this template, but because of the Not Laws, you can deduce that one of G, H, and L is placed on the bottom shelf:
Template #3: 2-2-4 Distribution
In this template, the FM block must be placed on the bottom shelf, which again opens the scenario up considerably. A number of possible solutions fit under this template, but because of the Not Laws, you can deduce that exactly two of G, H, and L are placed on the bottom shelf:
With the three templates in place, we are ready to attack the questions.
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