This is a Grouping: Defined-Moving, Unbalanced: Overloaded, Numerical Distribution game.
This is a very challenging game. Initially, the game looks like a standard Overloaded Grouping game:
Because each selection has two characteristics—type of stone (ruby, sapphire, topaz) and a specific name (F, G, etc)—there are two spaces for each of the six selections.
The first rule reserves at least two of the six selections for topazes:
Note that the rule is somewhat open-ended as it specifies that at least two of the topazes are selected, so the above diagram only represents the minimum that must occur.
The second rule is conditional:
- 2S 1R
Of course, if exactly two sapphires are selected, and exactly one ruby is selected, then the remaining three stones must be topazes:
- 2S 1R 3T
Thus, if exactly two sapphires are selected the six stone types are fully determined. More on this rule in a moment.
The third rule contains two negative grouping relationships:
- W H
W and H are different types, so tracking this rule is a bit more challenging. W and Z are both topazes, and thus the maximum number of topazes that can be selected is three: X, Y, W/Z. In turn, this affects the second rule, which results in the topazes being selected. If the second rule is enacted, then the three topazes must include X and Y:
- 2S 1R 3T (X, Y, W/Z)
Note that because at least two topazes must be selected from the first rule, and W and Z cannot both be selected, we can infer that X or Y or both must always be selected.
The fourth rule is a simple conditional rule:
- M W
Of course, W appears in both the third and fourth rules, and combining those two rules leads to the following two inferences:
- M H
Given that the first two rules address the number of each stone type in the game, a quick review of the numerical facts is worthwhile:
- Minimum 2 T (from the first rule)
Maximum 3 T (W and Z won’t go together, making 4 impossible)
Maximum 3 R (there are only 3 Rs)
Maximum 3 S (there are only 3 Ss)
2S 1R 3T (thus a 2-2-2 distribution is impossible)
Using these restrictions, the following Numerical Distributions can be identified:
The variety of distributions is one reason this game is difficult, but, fortunately, the distributions can be used to answer both question #14 and question #16.
Adding all of the information together produces the final setup: