# If both parks are planted with sycamores, which one of the following could be true?

Ryan on April 20, 2019

How?

How did you deduce the options to two scenarios? I got one scenario that was G: S M (M/S/T) L: S _ _ Both parks have Sycamores. That was the question prompt. So that condition is satisfied. Rule 1: S&M must be present in at least one park. Satisfied by G. Rule 2: O -> T. Since there is no space for O in park G then it can only be M/S/T. Satisfied. Rule 3: M is in park G. Satisfied. So, how did you deduce that there were two scenarios? I only got one scenario with multiple options. Please explain. Ty.

Replies

Ryan on April 20, 2019

Also, no where does it say in the question that all 4 variables need to be used or that they only appear once. all it says is that 4 trees are available.

Shunhe on January 12, 2020

Hi @maybeillgetlucky,

Thanks for the question! I think that your definition of a â€œscenarioâ€ just encompasses more than the instructorâ€™s definition of a â€œscenarioâ€ does (assuming youâ€™re talking about the video explanation for this question).

First, let me clear up your second question about all 4 variables needing to be used or that they only appear once. Itâ€™s definitely true that weâ€™re not told that all 4 variables need to be used. However, the variables can only appear once on each side. Take a look at the first ruleâ€”each of the parks is planted with exactly three of the varieties. The list we are given of maples, oaks, sycamores, and tamaracks lists different varieties of trees. Thus, we know that in a single park, there have to be three different letters, because planting the same variety twice (like planting maples and maples) is really just planting the variety once (since theyâ€™re both maples). The varieties have to be unique in each park, and this is part of what may have confused you.

Knowing this, we can take a look at the instructorâ€™s scenarios, which are

G: MST
L: SOT or MST

And this is what she refers to as two scenarios. You seem to have in mind one scenario where itâ€™s

G: SMT (knowing now that the rule only allows for unique letters in each park
L: S _ _

And this is kind of equivalent to the instructorâ€™s, although you did miss out that T has to be in L, probably because of your confusion with Rule 1. Since we know that S is already in park L, we have to choose 2 of the 3 remaining trees for park L. If we plant O, that means we have to plant T, so one of the options is SOT. If we donâ€™t plan O, by default, we pick the other two, and so we pick MST. So really, we can think of L as

L: ST M/O

And whether you call that two scenarios or one scenario with multiple options is really just a matter of semantics. Hope this helps! Feel free to ask any other questions that you might have.