If Lan does not lead a Wednesday session, then which one of the following lab assistants must lead a Thursday session?

Ava on March 22 at 07:34PM

Approach

Can some explain how they solved this question? I’m having trouble approaching it.

1 Reply

Skylar on March 22 at 09:09PM

@shafieiava, happy to help!

Let's start with the game setup:

JKLNOR
AM __ __ __
PM __ __ __
W T F

Rule #1: We must either have K or R
R K
Rule #2: We cannot have L or O
O. L
Rule #3: N = PM
Rule #4: J = at least one day before O. I did not write this as J>O because I wanted to be sure to remind myself that we are talking about days, not just time slots.

Before proceeding to the questions, we should look for deductions we can make. Rule #1 tells us that K and R must go on the same day, which is a significant restriction. We should try to start there. Let's set up a few hypotheticals:

HYPO 1:
Let's see what happens if we place K and R on Wednesday. Remember, we don't know which variable is assigned to which slot on Wednesday. This gives us:
AM (K/R) __ __
PM (R/K) __ __
W T F
Rule #4 tells us that J is on an earlier day than O, so we know that J will go somewhere on Thursday, while O will go somewhere on Friday. This gives us:
AM (K/R) (J/?) (O/?)
PM (R/K) (?/J) (?/O)
W T F
Rule #2 tells us that L and O cannot go on the same day, so L must be assigned to Thursday. This leaves N to fill the last spot on Friday. Rule #3 tells us that N must go in the afternoon spot, which means that O must go in the morning spot. This gives us:
AM (K/R) (J/L) O
PM (R/K) (L/J) N
W T F

HYPO 2:
We can place K and R on Thursday and go through the same steps above to get:
AM (J/L) (K/R) O
PM (L/J) (R/K) N
W T F

HYPO 3:
We can place K and R on Friday and go through the same steps above to get:
AM (J/L) O (K/R)
PM (L/J) N (R/K)
W T F

These three hypotheticals set up all of our game possibilities and will save us significant time and effort when answering the questions. We were tipped off to setting up the hypotheticals by the significant restrictions imposed by the rules. However, if you did not get the hypotheticals when you completed the game, don't worry. It is still very possible to complete the game on time without these scenarios.

Now to the question: "If Lan does not lead a Wednesday session, then which one of the following lab assistants must lead a Thursday session?"

If we were able to deduce the hypotheticals above, we could solve this by referencing HYPO 1, which is the only hypothetical in which L is not assigned to Wednesday. In this, L and J lead the Thursday sessions. Therefore, the correct answer is (E) J.

If we did not make the hypotheticals, we can work through this question as follows:
- If L is not on Wednesday, that means he is either on Thursday or Friday.
- It is impossible to place L on Friday. This is because P and G will always be on the same day (Rule #1), O and N will always be on the same day (because Rule #2 says that O and L cannot be on the same day, Rule #4 says J is on a different day than O, and we have limited options), and L and J will always be on the same day (because Rule #2 says that O and L cannot be on the same day, Rule #4 says J is on a different day than O, and we have limited options). J cannot be assigned to Friday because Rule #4 says that J is always at least one day earlier than O. This means that L cannot be on Friday.
- Therefore, if L is not on Wednesday, he is on Thursday.
Let's draw this out:
AM __ (L/?) __
PM __ (?/L) __
W T F
As we established above, J and L will always be paired together. This gives us:
AM __ (L/J) __
PM __ (J/L) __
W T F
We can stop here, as we know our Thursday assignments are J and L. Of these, only J is an answer choice. Therefore, (E) "J" is correct.

Does that make sense? Please let us know if you have any other questions!