Thanks for the question! Strictly speaking, it’s not the number of conditional rules that limit our ability to do scenarios—there are some games with a lot of conditional rules that end up restricting the board in such a way that there are a limited number of scenarios, and it’s possible to diagram them out. The problem with this game is that there are a decent number of scenarios to diagram out.
That being said, it wouldn’t be the worst thing to diagram out partially the case in which Maricella plays golf and the case in which Maricella plays tennis, since we know one of these two cases has to happen. Past that, however, there are a lot of moving parts: each player can play one of two sports, and has to be ranked in a certain order within that sport. It can get complicated making those scenarios, and so after some of the initial scenario-making like I suggested above, you don’t want to get too into the weeds and move onto the questions. But beginning with, for example, the Maricella scenarios and mapping those out to some extent is helpful for this question.
Hope this helps! Feel free to ask any further questions that you might have.
IrinaMarch 29, 2020
Hi @kassidee,
That's right, it would be too time-consuming to come up with all the possible scenarios during the setup. We have the following rules:
K L M O P S
G: L =1 T: O
M :G -> P & S : G M > P > S
M: T -> O > S > M
P:T -> K:T K > O > P
To summarize the rules we could come up with three base diagrams without writing all the possible options:
(1) M plays golf. In this scenario, the only free variable is K that could either play G or T and it is ranking is unknown.
G: L M P S /K T: O /K
(2) M plays tennis and P plays golf.
G: L P /K T: O S M /K
(3) M plays tennis and P plays tennis. In this scenario, we can determine the sport each person plays but not the exact rank of tennis players.
G: L T: K O S M P
Looking at the questions, question 1 asks which of the following could NOT be the lowest ranking tennis player.
Per the diagram above, K could have any rank, P could be the lowest in scenario 3, M could be the lowest in scenario 3 as well. O could be the lowest in scenario 1 if K is ranked higher than him. Hence, S is the only one that could not be ranked the lowest because he must be ranked higher than M (A).
Question 2 asks which of the following could be a list of people playing tennis ranked from highest to lowest.
Per scenario 2, O S K M could be a complete and accurate list of tennis players (D)
Question 3 asks if S plays golf, then which of the following pairs does NOT have to play the same sport.
We can see that the only option when S plays golf is scenario 1 when M also plays golf as well as L and P, thus we can eliminate option (A), (B), (D), and (E). (C) is the only possible option as K is a free variable and could play T instead.
Question 4 asks if O is the highest ranking tennis player, which of the following must be true?
O could be the highest-ranking player in scenario 1 or 2, in both of these scenarios P & L must play golf (option B)
Question 5 asks if the condition is added that S and P do not play the same sport as each other, each of the following could be true EXCEPT. This is scenario 2 above, if P and S do not play the same sport as each other, then P and M must also play different sports (C).
Question 6 asks which of the following could be true? We can see from the three diagrams above that the only option that could be true is (C) K plays T and P plays G.
Let me know if this makes sense and if you have any other questions.
kassideeMarch 29, 2020
Isn't writing a "base diagram" the same as writing scenarios since scenarios don't show all possibilities?
shannonk68September 11, 2020
I'm confused by how the answer is Kim plays tennis and Paulo plays golf when in the set up the contrapositive of if Paulo plays Tennis then Kim Plays Tennis is Kim plays golf then paulo plays golf?
