Setup and Rule Diagrams

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Setup and Rule Diagram Explanation

This is a Grouping: Unbalanced, Partially Defined game.

The game scenario establishes that each of three bouquets (1, 2, and 3) must have at least one of five kinds of flowers—lilies, peonies, roses, snapdragons, and tulips:

PT73_Game_#4_setup_diagram 1.png

The scenario does not require that we use all five of the flowers in creating the bouquets, nor does it limit the number of times each flower can be used. This type of uncertainty makes the game Unbalanced, and presents an exceptionally large number of Numerical Distributions that we cannot analyze in the time allotted. In addition, we are only given the minimum number of flowers per bouquet (one), which makes the game Partially Defined.

The first rule states that bouquets 1 and 3 cannot have any kind of flower in common:

PT73_Game_#4_setup_diagram 2.png

The second rule stipulates that bouquets 2 and 3 must have exactly two kinds of flowers in common, which also means that each of these two bouquets must have at least two kinds of flowers in it:

PT73_Game_#4_setup_diagram 3.png

The third rule states that bouquet 3 has S:

PT73_Game_#4_setup_diagram 4.png

Of course, just because bouquet 3 has S does not mean that bouquet 2 does also. The second rule requires that the two bouquets have exactly two flowers in common, not that they have exactly the same kinds of flowers. Either bouquet can have flowers that are unique to that bouquet. However, you should immediately notice the implication of the third rule on bouquet 1: if bouquets 1 and 3 cannot have any flowers in common, then bouquet 1 cannot have S.

PT73_Game_#4_setup_diagram 5.png

The fourth rule uses conditional reasoning and can be diagrammed as follows:

PT73_Game_#4_setup_diagram 6.png

Double necessary conditions are sometimes confusing, especially when they have opposite values. While somewhat unorthodox of an approach, here it makes sense to split the rule into two separate conditional statements, in order to simplify its application:

PT73_Game_#4_setup_diagram 7.png

Consequently, because bouquet 3 must have S, it cannot thereby have L:

PT73_Game_#4_setup_diagram 8.png

The last rule establishes another conditional relationship, this time between T and P:

PT73_Game_#4_setup_diagram 9.png

The final diagram of this game should look like this:

PT73_Game_#4_setup_diagram 10.png

Given the exceptionally high level of uncertainty inherent in this setup, you should expect that the questions will be time-consuming. Thus, as long as you have a solid understanding of the rules, it would be best to attack the questions head-on.