If no two live calls are aired consecutively and no two taped calls are aired consecutively, then in exactly how many...

shunhe on August 5, 2020

Hi @Eliyahu-Ohevshalom,

Thanks for the question! So we’re told in this question that no two lives calls are aired consecutively and no two taped calls are aired consecutively. Recall that the third call is from K and is taped.

Well, based on the rules we got, that means 2 and 4 have to be live (since there can’t be two taped calls next to each other). And that means 1 and 5 have to be taped, since we can’t have two lives calls next to each other! So we know the following:

T L T L T
_ _ K _ _
_ _ H _ _

We know that H is third because I and M are the first two, and H goes before F and G. Well, we know that both S calls are live, so S has to be in slots 2 and 4! And we know M and F don’t call from S, which means that in this case, it has to be G and I (because the first two are I or M, and the last two are F or G). But since we’ve placed G and I, we can also place F and M! And we also know that since we’ve placed K and the two S’s, we can also place the two Vs! So now we have

T L T L T
V S K S V
M I H F G

Which means that there’s only one solution to this game given the hypothetical, and so (A) is the correct answer.

Hope this helps! Feel free to ask any other questions that you might have.