Logic Games Random Mix - - Question 4

If Henri were to use exactly three appliances, then what is the total number of different groups of three appliances ...

Joyce August 19, 2020

Why would it not be 3?

Why would it not be 3?

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shunhe August 19, 2020

Hi @Joyce,

Thanks for the question! So we’re saying that Henri uses exactly 3 appliances, and trying to figure out what the possible groups of appliances are that he can use in this group of 3. Well, remember, when Henri uses V, we have from the third rule

V —> ~H & ~R & ~T

So when Henri uses V, we can’t use 3 of the other things, which means at most two things can be picked. So V can’t be in a group of 3.

Also notice that when Henri uses H, he can’t use R or T from the first two rules, and can’t use V from the contrapositive of the third rule. So again, when Henri uses H, we have to throw out 3 variables, which means that there’s only 2 left, and H can’t be part of a group of 3.

But that means there’s only 3 variables left that can be part of a group of 3: T, R, and M. Do these work together? Yes, and there’s only one way to pick three things out of three (you pick all of them). So the answer to this one is there is one possible grouping.

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

Lenny April 28, 2021

I think he meant why is it worded like that when it can be TMR RTM and MTR which is confusing because it doesn't specify what a "group" means. I understand that the question doesn't express any concern for the order of the products so it is logical to pick one and not three, but that is what I believe he is referring to.