A,B,C linkage example

[DavidW]

P. 294 of Logic Games Bible 2018 talks about a linkage inference: If AB in car 2, then CDE in car 1, and if AB in car 1, then one of CDE in car 1 and the other two in car 2.

It then says, "...we have discovered a controlling inference in the game, and one that we could display in our diagram." I was curious how you might go about diagramming something like this? I feel like there are lots of times that I can make an inference, but I can't figure out how to diagram it, but if I just try to hold the inference in my head, I forget it by the time I'm working on the questions. I'd love to see an example for how the above inference could be diagrammed. Thanks!

[Jonathan Evans]

Hey David,

Great question! You definitely don't want to hold too much in your head. As you've likely observed, trying to keep track of too much information and too many observations can be an impediment while you're working through games. In addition, we're prone to making small mistakes that have bad consequences if we try to juggle too much at the same time.

In other words, your insight is correct, let's put pencil to paper and make these diagrams explicit. In a scenario similar to the one described on page 294, you'd likely use two templates to depict both possibilities. Your diagramming could look like this:



Start with your core setup and rules. Notice that we've assigned the slots for the adult passengers but have left an area blank for the children in each car. The game does not stipulate that each car must contain any number of children (or any at all; it is undefined), so we're going to leave that aspect open-ended.

Next, as you are considering the implications of the rules, it will become apparent (as in the discussion on 294) that things will split exactly one of two ways: either A and B will be together in car 1 or they will be together in car 2. In a situation such as this in which this split has profound implications on the remaining arrangement, you will almost certainly wish to depict both possibilities.

I'm partial to naming my templates after Greek letters, but that's just me. I've called them alpha and beta.

Now whenever I'm doing a question, whether global or local, one of the first things I'll consider is whether I'm dealing with my alpha template, my beta template, or possibly both.

These situations are common but not exclusive to grouping games. One of my favorite examples of a game like this is the recipes grouping game, PrepTest 24, Game 1.

Please follow up with further questions!

[DavidW]

Perfect. When the book read, "...we have discovered a controlling inference in the game, and one that we could display in our diagram," I was thinking that there was some way to display this inference in one diagram, which threw me for a loop. However, if we instead say that we're going to display it in two templates, then it makes sense. Thanks!