Great question. If you build out your hypothetical game boards well after reading the rules, there is a very fast way you can answer this question. But first, let's make sure we are setting up the game properly.
We're told that there are 5 pieces (F, L, M, P, and S) in a mailbox going to 3 different people (g, j, and r). We know that each person receives at least 1 piece of mail, and all of the pieces of mail are used.
g j r _ _ _
Rule 1 says L and M can't go in g. This means that L has to go in j or r and M also has to go in either j or r
1) L j/r M j/r
Rule 2 says if L is in r, then P is in j
2) Lr - >Pj /Pj - >/Lr
Rule 3 says F must be with at least one other piece of mail
3) F not solo
Now it's time to take the rules and see if we can split the game board into multiple hypotheticals.
In looking at our rules, rules 1 and 2 appear to be great places to split since L has to be in j or r and L is also involved in a conditional relationship with P. Let's put L in j in one game board and L in r in the other
g j r _ L _
g j r _ _ L
For the top game board, rule 2 falls away because the sufficient condition is failed. For the bottom game board, rule 2 is triggered, so P must go into j
g j r _ L _
g j r _ P L
In both game boards, M can go in either j or r. Additionally, we just need to place F with at least one other piece in both game boards.
That leaves us with S. If we look at the bottom game board, g is still empty and it needs at least one piece. M can't go in there since it has to be in j or r. That means that either F or S must go in g. However, if F goes in g, it has to come with someone else, so S must go in there. Alternatively, if F goes somewhere else (j or r), then S must go in g to give g at least one piece, so we know that S must be in g no matter what in the bottom game board.
g j r _ L _
g j r S P L
Now we know that for the top game board, M has to go in j or r, F must go with at least one other piece, and P and S are floaters.
For the bottom board, F and M are now both floaters.
Let's look at the question now. The question asks, "Which one of the following CANNOT be a complete and accurate list of the pieces of mail addressed to Jana?"
As you noted, we could test out all of the different scenarios to get the right answer. However, the faster way to do this problem is to look at our game boards and recognize that j must have either L or P in it. (E) does not include either L or P, so we know that this is a list that WOULD NOT WORK for j since j needs to have either an L or P.
Does this make sense? Let us know if you have any more questions!
Jersson-MorochoFebruary 2, 2019
Yes, thank you that helped a lot!
RaviFebruary 10, 2019
@Jersson-Morocco, happy to help!
sergeiJune 18, 2020
You should consider replacing the current video with this one, it seems much faster and closer to what the lesson videos want us to deduce
