Missing crucial inference

[kirilrez]

The problem is attached-


Here I picked the correct answer, but not quite sure why the other option is incorrect.

What I thought as I was picking the answer- is that one N is already there and there are two more squares with 2 dots, so it makes sense that they would also be N.

J is two dots because you can't have him on Thursday and therefore L is three dots.

But, my problem is with the dot notation- why do you need it - why just not write the letters, what are its benefits?

What prevents 2 squares with a different pattern of dots from representing the same letter?
I get it wouldn't make sense, but still am confused by it.

[noah]

Thanks for the question. The dot notation is to represent the idea that the element can't be the same in two groups. So, in this example, T has two different element types, one of which W has. Th has a third type (not J).

We can infer that either J is in T, and could be in W as well.

The idea of the dots is to note relationships without committing to a certain letter. For example, if the rule is W and T share one element in common, the dots do a nice job of noting that. In this case, the diagram is not complete since you could infer that J is in T, but the game isn't designed to necessarily have complete diagrams.

The other thing that's nice about the dots is that you can tell when all the elements will be used. In this case, since we see a 1-dot box, a 2-dot box, and a 3-dot box, we know that all 3 elements must be used in among those boxes. Thus, we can't have only 1 N assigned since we see one already and one must be among those three differently-dotted boxes (new phrase I just invented!). It seems like you hit on that inference your own way.

I hope that helps.