Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Defined-Fixed, Balanced game.

The first key to this game comes from the second rule, and involves physically placing a G/M dual-option into both groups. This placement serves as a visual reminder that one space is already occupied in each group by either G or M. Thereafter, the basic setup and rule representation is fairly straightforward:

D94_Game_#1_setup_diagram 1.png

Next, let us examine some of the important inferences that can be drawn from the rules:

This Defined Grouping game involves placing 8 variables into 8 positions. Because all 8 variables must be in one of the two groups, the game uses a two-value system, which means that if a variable is not in one group, then it must automatically be in the other. Because of this feature, the second key to the game comes from taking the contrapositives of the third and fourth conditional rules and then translating them to account for the two-value system:

D94_Game_#1_setup_diagram 2.png

Thus, when H is in group 1, then L is in group 1. Via the translated contrapositive, when L is in group 2 then H is in group 2. Does this mean that H and L are always a block? No, because L could be in group 1 and H could be in group 2.

D94_Game_#1_setup_diagram 3.png

Thus, when N is in group 2, then G is in group 1 (and, incidentally, from the second rule, M is in group 2). Via the translated contrapositive, when G is in group 2 then N is in group 1 (and, incidentally, from the second rule, M is in group 1). Does this mean that N and G are always in separate groups? No, because G could be in group 1 and N could be in group 1.
The third rule allows for another inference. Because of the limited number of spaces per group, we can further deduce that if H is in group 1 (that is, the third rule is activated and thus L is also in group 1), then the FJ block created by the first rule must be in group 2 (remember, G or M is also in group 1, so there is only one remaining space when H and L are in group 1). Also, if L is in group 2, then H is in group 2, and the FJ block must be in group 1. These two inferences can be diagrammed as:

D94_Game_#1_setup_diagram 4.png

With the above information, we are ready to attack the questions.

[bwise2928]

Hello,

Why can't an inference be made than M & N have to be together? According to rule 4, N2 ---> G1 and based on rule 2, G and M can never be together. So couldn't you infer that N2 ---> not M1 (contra: M1 ---> not N2) which translates to N2 ---> M2 (contra: not M2 ---> not N2) and translate that even further into M1 ---> N1?

Definitely confused, any help would be appreciated, thanks!

[Adam Tyson]

Good question, bwise2928, and the answer comes from looking at what happens when the rule is not triggered. When N is in Group 1, it has no effect on G, so G could be in either group, and therefore M could also be in either group. It's possible that N and G are both in Group 1 while M is in Group 2!