Which one of the following could be an accurate list of the cars in the order in which they are washed, matched with ...

Victoria on June 20, 2021

Hi @Ajax0815,

Happy to help!

We learn that five cars will be washed, each exactly once: F, M, O, T, and V.

Each car will be washed one at a time and each car will receive exactly one kind of wash: R, S, or P.

Therefore, this is a multi-linear game. We have one row for car and the other for type of wash.

_ _ _ _ _
_ _ _ _ _
1 2 3 4 5

Now let's go through our conditions.

Rule 1 - Car 1 does not receive an S wash, though at least one car does.

Therefore, Car 1 must receive either an R or a P wash.

Rule 2 - Exactly one car receives a P wash.

Rule 3 - Cars 2 and 3 receive the same kind of wash as each other.

This means that neither Car 2 nor Car 3 can receive a P wash because Rule 2 tells us that exactly one car receives a P wash.

Therefore, Cars 2 and 3 must receive either an R or an S wash.

Rule 4 - Neither O nor T is washed before V.

> O
V
> T

Rule 5 - M is washed before F but after O

> O > M > F
V
> T

Therefore, V must be washed first. This means that V must receive either an R or a P wash.

Rule 6 - M and the car washed immediately before M receive R washes.

Based on the order we have outlined above, either O or T could be washed immediately before M. Therefore, either O or T also receives an R wash.

So, what do we know so far?

V _ _ _ _
R/P R/S R/S _ _
1 2 3 4 5

Based on what we know, we can outline a few different scenarios.

Scenario 1:

V T O M F
P R R R S
1 2 3 4 5

We know that M and the car washed immediately before M (in this case, O) receive R washes. We also know that Car 2 and Car 3 must receive the same wash. This means that T must also receive an R wash.

Rules 1 and 2 tell us that at least one car receives an S wash and exactly one car receives a P wash. We know that Car 1 cannot receive an S wash. Therefore, Car 1 must receive a P wash and Car 5 must receive an S wash.

Scenario 2:

V O T M F
P R R R S
1 2 3 4 5

This is the same as the scenario above, but O and T have switched places.

Scenario 3:

V O M T F
R/P R R R/P/S R/P/S
1 2 3 4 5

This scenario leaves a bit more open. All we know is that O and M must both receive R washes.

Scenario 4:

V O M F T
R/P R R R/P/S R/P/S
1 2 3 4 5

This scenario is the same as the one above, but F and T have switched places.

So, we have two scenarios that are fully mapped out and two which are a bit more open-ended.

Answer choice (A) is incorrect because O's car is washed before V's, violating Rule 4.

Answer choice (C) is incorrect because M's car is washed before O's, violating Rule 5.

Answer choice (D) is incorrect because Car 1 receives an S wash, violating Rule 1.

Answer choice (E) is incorrect because no cars receive an S wash, violating Rule 1.

Answer choice (B) is correct because it directly mirrors Scenario 2 that we have outlined above.

Hope this helps! Please let us know if you have any further questions.