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#26015
Setup and Rule Diagram Explanation

This is a Grouping/Linear Combination, Numerical Distribution game.

This game asks us to assign each of six sections to one of three consecutive aisles. Because the aisles have an inherent order, our initial setup for the game should appear as follows:
oct12_game_3_diagram_1.png
oct12_game_3_diagram_1.png (2.28 KiB) Viewed 2712 times
The game scenario indicates that each aisle contains at least one section, but no maximum requirement of sections per aisle is established. Thus, the following unfixed numerical distributions of sections to aisles are possible:
  • ..... ..... ..... ..... ..... ..... 4-1-1

    ..... ..... ..... ..... ..... ..... 3-2-1

    ..... ..... ..... ..... ..... ..... 2-2-2
The remaining rules do not have further impact on the number of possible numerical distributions, and the three distributions above are the only distributions possible in the game. However, additional information can be determined about some of the distributions based on the rules.

The first rule requires R to be located in the same aisle as either F or M. Given the horizontal orientation of our setup, we need to use a vertical block to indicate identicalness or similarity:
oct12_game_3_diagram_2.png
oct12_game_3_diagram_2.png (1.7 KiB) Viewed 2712 times
The second rule establishes that F is located on a lower-number aisle than both M and P. Since our aisles are numbered from 1 (lowest) to 3 (highest) with numbers increasing to the right, the sequence should place M and P to the right of F:
oct12_game_3_diagram_3.png
oct12_game_3_diagram_3.png (1.82 KiB) Viewed 2712 times
This sequence creates three Not Laws on the diagram—an F Not Law, an M Not Law, and a P Not Law:
oct12_game_3_diagram_4.png
oct12_game_3_diagram_4.png (2.26 KiB) Viewed 2712 times
The third rule creates another sequence:
  • ..... ..... ..... ..... ..... S :longline: P
This sequence adds an S Not Law to the diagram (we already have P as a Not Law from the second rule):
oct12_game_3_diagram_5.png
oct12_game_3_diagram_5.png (2.53 KiB) Viewed 2712 times
Additionally, because both the second and the third rules contain P, they can be linked together to create a super-sequence:
oct12_game_3_diagram_6.png
oct12_game_3_diagram_6.png (2.41 KiB) Viewed 2712 times
The fourth rule tells us that S cannot be in a lower-numbered aisle than H:
oct12_game_3_diagram_7.png
oct12_game_3_diagram_7.png (1.4 KiB) Viewed 2712 times
You should immediately turn this rule into a positive statement: if S cannot be in a lower-numbered aisle than H, it logically follows that S must either be located in the same aisle as H (i.e. aisle 1 or 2), or else be in a higher-numbered aisle than H:
oct12_game_3_diagram_8.png
oct12_game_3_diagram_8.png (1.14 KiB) Viewed 2712 times
Either way, since S cannot be located in aisle 3, we can infer that H cannot be located in aisle 3 either. This limits which sections can be placed in aisle 3 to M, P, and R:
oct12_game_3_diagram_9.png
oct12_game_3_diagram_9.png (3.47 KiB) Viewed 2712 times
We can also add the last rule to our super-sequence:
oct12_game_3_diagram_10.png
oct12_game_3_diagram_10.png (2.81 KiB) Viewed 2712 times
While this sequence produces a number of Not Laws, it does not allow us to place any of the five variables in a particular aisle. Additionally, the vertical block is not as helpful as we would normally expect, because R’s placement relative to the rest of the variables is unknown. Finally, a closer inspection of the three Numerical Distributions reveals that only one of them (2-2-2) is sufficiently defined, which we discuss in question #15. Despite the distributions, the game is not sufficiently restricted to allow for a Templates-based approach. Thus, our final diagram looks like this:
oct12_game_3_diagram_11.png
oct12_game_3_diagram_11.png (9.54 KiB) Viewed 2712 times
Do not let the loosely-defined nature of this setup concern you: a quick glance at the questions reveals that the vast majority of them are Local, and as such further limit the range of possible solutions. The only Global question is question #16.

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