Which one of the following could be an accurate ranking of all the crews, in order from first to sixth, for a given w...

on December 24, 2019

Can we get some help on this game?

On the surface, this should seem to be a simple sequencing game. For me, it was anything but. Can we/me get some help with this?


Irina on December 24, 2019


The game requires us to rank the productivity of six crews - F G H R S T from 1st to 6th. Two of the crews are night shift crews - either G & T or S & H - and the remaining 4 are day shift crews. In other words, there are two possible scenarios:

G T - night, F H R S - day
S H - night, F G R T - day

__ __ __ __ __ __
1 2 3 4 5 6

The following rules apply:

(1) F > G
(2) R > S
(3) R > T

R > S
> T

(4) S > H
R > S > H
> T

(5) G > T
F > G > T

So overall, we have the following two chains:

R > S > H

F > G > T

Question 1 asks us which of the following could be an accurate ranking of all the crews for a given week?

(A) is incorrect because R >T
(B) is incorrect because S > H
(C) is incorrect because F > G > T
(D) is correct and complies with all the rules
(E) is incorrect because G > T

Question 2 asks if F is ranked third, then which of the following could be true?

Well if F is ranked third, and G & T have to come after it they must be ranked either 4th and 5th or 5th and 6th

R S F ___ ___ __
/G G/T /T
/H /H
R and S must be # 1nad #2, and H is a free variable that could be either fourth or sixth.

The only answer that could be true is (B) - H is ranked fourth, or alternatively it could be ranked sixth.

Question 3 asks which of the following CANNOT be the crew ranked fifth for any given week of the study?

Considering we have these two chains

R> S >H
> T

F > G >T

we can tell that R or F can never be ranked fifth because at least two crews must come after them (answer choice (C)

Question 4 asks for any given week of the study, the ranking of all crews is completely determined if one of the following is true.

Since H must be preceded by R &S , we know that if H is ranked third, R & S must be ranked first and second, and F G T must be 4th, 5th and 6th respectively (C).

Question 5 asks if the night crew rank fifth and sixth for a week, then which of the following could be true.

So in other words if G &T or S & H rank last, which of the following could be true.

Let's consider both scenarios:

__ __ __ __ G T
R > S> H

__ __ __ __ S H
F > G> T

We can see that (A), (B), (D) , and (E) are impossible in both scenarios. Only (C) - R could rank third could be true:

F G R T S H .

Question 6 asks which of the following crews cannot rank third?

We know that R could be third from the previous question, so we can right away eliminate (B). We can also see that H could be third from our scenario above, thus we can eliminate (A). We can also see that G could be ranked third - R F G T S H, thus we can eliminate (D) and finally, we can eliminate (C) - R S F H G T could be true per our scenario above. Hence, the only one that could not be third is T (E).

on December 24, 2019

Thank you. Keeping the chains separate in this game, at least to me, made it clearer as to questions 2, 3, and 4. By trying to create a longer chain, thereby bring the crossover of T into the visual for me, created too many complications for the HGT relationships. In your answer to 3 above, you have G/T as possible for 4. But isn't H also a possibility for 4 since, as you say, H is a free variable? Thanks again.

Irina on December 25, 2019


I am assuming you are asking if H could be #5. Yes, H could also be 5th, or 4th or 6th. Good catch!

on June 9, 2020

Hi @Irina - many thanks for the above, that's helpful. Please could you explain further how to deal with the crews that are night shift crews - (G & T or S & H ) - how do you approach this in terms of the number line? I see that you broke this out into two separate chains, but grateful if you could please explain further. Many thanks!