- Thu Mar 21, 2013 11:53 am
#94348
Setup and Rule Diagram Explanation
This is a Grouping: Defined-Fixed, Balanced game.
The game scenario establishes that eight people—three adults and five children—will be assigned to two groups of four people each:
Because there are only two groups, and every variable must be in one of the two groups, the groups form a two-value system, which plays a major role in the game.
The first rule establishes that each boat is assigned at least one adult, so reserve a space in each boat for F, G, and H:
The second rule is conditional:
Of course, because the game is a two-value system, when we take the contrapositive, we can convert the negatives into positives by changing the boat number (if G is not in boat 2, then G must be in boat 1, etc):
Note that this rule (and its contrapositive) does not imply that F and G are always in the same boat. For example, G could be in boat 2 and F could be in boat 1.
The first two rules can be combined to create two inferences. When F is assigned to boat 2, G is assigned to boat 2, and because there must be an adult in each boat, H must then be assigned to boat 1.
Similarly, using the contrapositive of the second rule, when G is assigned to boat 1, F is assigned to boat 1, and then H must be assigned to boat 2:
The contrapositive of these last two inferences, again accounting for the two-value system:
The third rule is similar to the second:
As always, make note of the contrapositive in any two-value system game:
Note that this rule (and its contrapositive) does not imply that V and W are always in different boats. For example, V could be in boat 2 and W could be in boat 2.
The fourth and final rule indicates that X and Z are in different boats. The best diagram for this rule is to place X/Z dual options on the main diagram, while also noting that Y is a random (while H is not directly named, H is covered under the actions of the first rule):
Combining all of the prior information leads to the final setup:
This is a Grouping: Defined-Fixed, Balanced game.
The game scenario establishes that eight people—three adults and five children—will be assigned to two groups of four people each:
Because there are only two groups, and every variable must be in one of the two groups, the groups form a two-value system, which plays a major role in the game.
The first rule establishes that each boat is assigned at least one adult, so reserve a space in each boat for F, G, and H:
The second rule is conditional:
Of course, because the game is a two-value system, when we take the contrapositive, we can convert the negatives into positives by changing the boat number (if G is not in boat 2, then G must be in boat 1, etc):
Note that this rule (and its contrapositive) does not imply that F and G are always in the same boat. For example, G could be in boat 2 and F could be in boat 1.
The first two rules can be combined to create two inferences. When F is assigned to boat 2, G is assigned to boat 2, and because there must be an adult in each boat, H must then be assigned to boat 1.
Similarly, using the contrapositive of the second rule, when G is assigned to boat 1, F is assigned to boat 1, and then H must be assigned to boat 2:
The contrapositive of these last two inferences, again accounting for the two-value system:
The third rule is similar to the second:
As always, make note of the contrapositive in any two-value system game:
Note that this rule (and its contrapositive) does not imply that V and W are always in different boats. For example, V could be in boat 2 and W could be in boat 2.
The fourth and final rule indicates that X and Z are in different boats. The best diagram for this rule is to place X/Z dual options on the main diagram, while also noting that Y is a random (while H is not directly named, H is covered under the actions of the first rule):
Combining all of the prior information leads to the final setup:
. 
= children
G
Z
. The bottom line is that the necessary condition doesn't rely on the sufficient condition for an event to happen and that the sufficient condition needs the necessary condition to make the event happen.