Minimum, Maximum Questions, Specifically on In-Out Games

[secretad22]

I have done the Souderton in-out game and bird in out game (with shrikes and such) and both of those had in-out games.

I am well aware of a rule such as:

A ---> ~B

This rule means that at least one of A and B must always be out, perhaps even both can be out.

So I know that in this situation in a hypothetical game, we could never have all of the variables in, at least one must always be out.

Now, after that point is where I struggle.

Do I make a hypothetical with A in and B out, or B in and A out.

I know that which one to pick to be in or out would be determined by other rules, but I feel uncertain how the rules will affect the overall number.

I always feel uncertain because I simply don't know if I could have fit an extra variable in somewhere with a different variable being out vs being in and vice versa.

Thanks guys.

[bbirdwell]

Great question! This is a really popular issue in in/out games (binary grouping, as we call them).

You're off to a good start with that inference about A and B. The next step would be to ask "can all of them but one be in?" And then, when choosing which one you might want to be "out" in that case, scan the constraints and choose one that doesn't seem to relate or affect other elements, if possible.

For example, if the first constraint says A --> ~B, and the next one says ~B --> ~C & ~D, then I wouldn't want A to be in if my goal was to maximize.

You can browse through the forum posts for the games you mentioned and download the diagrams. The Logic Chain is our preferred method for diagramming these types of games, and it creates a great visual overview of the constraints, so that considering min/max questions can be done without having to write out a bunch of test cases in linear fashion. Check them out and see what I mean...