# Which one of the following could be the order in which the programs are shown, from earliest to latest?

Saja on May 29, 2018

Explanation

Could you please provide an explanation for this game. I am not sure how to go about it in a more efficient way.

3 Replies

Christopher on June 6, 2018

@Saja, this is a linear game, so set it up as such and start diagramming the rules.
_ _ _ _ _ _
1 2 3

Rule 1 says G must be on the hour, so it cannot start at 1:30, 2:30, or 3:30.
_ _ _ _ _ _
1 2 3
G G G

Rule 2 is that T starts on the half hour, so cannot start at 1, 2, or 3.
_ _ _ _ _ _
1 2 3
T G T G T G

Rule 3 is Roamin' before Sundown (R_ _ _ _ _ _
1 2 3
T G T G T G
S R

Rule 4 is if Waterloo is before Terry, it is immediately before Terry so W [WT]. This also means that if W comes before T, then W must start on an hour when it comes before T.

That's the basic setup, so let's get into questions.

Question 1 asks which could be a possible order, so rule out each answer by going through the rules from start to finish.

Rule 1 says G is on the hour, which takes out (C).

Rule 2 says T is on the half hour, which takes out (A).

Rule 3 says R
Rule 4 says W [WT], which takes out (D).

Which leaves (B) as the correct answer. Write out that hypothetical under your diagram and move on.
_ _ _ _ _ _
1 2 3
T G T G T G
S R
______________
R S W T GG

Question 2 places W in 1 and asks how many possible orders are left. W in 1 forces T to be 1:30. We also know G must start on the hour, so it must be at 2 or 3. R must come before S, so they will be stuck back to back either at 2 or at 3. So you have two possible options, so the answer is (B).
WT RS GG or WT GG RS
Put both on your diagram and move on.
_ _ _ _ _ _
1 2 3
T G T G T G
S R
______________
R S W T GG
W T R S GG
W T GG R S

Question 3 puts R in the second slot, which should be 1:30 or 2, depending on if G is first. However, since T cannot be on the hour, it cannot be the first show. W cannot be the first show unless T is the second show, which is precluded by R being second. Finally, S cannot come before R, so G must be the first show, and R must start at 2:00.

GG R_ _ _

So then go through the answers and eliminate what IS possible.

(A) S needs to come after R, so it can be at 2:30 without any issue. GG RS WT.

(B) S can also come 4 as long as T comes before W. GG RT SW.

(C) T can be fifth as seen in (A)'s hypothetical.

(D) placing W in slot 3 would put it ahead of T, and if that is the case, T must come immediate after W. T cannot start on the hour, so W cannot be third and (D) is the correct answer.

(E) W is the last show is shown in the (B) hypothetical.

_ _ _ _ _ _
1 2 3
T G T G T G
S R
______________
R S W T GG
GG R S WT
GG R T SW

Question 4 puts S in slot 3. The GG RS WT hypothetical gives us one example, so we can eliminate (B) immediately because R can be somewhere other than slot 1.

There are other possibilities though, so what if you put R in 1 and S in 3? Rule 1 would then require G to be in slot 5, and rule 4 would place T in slot 2 and W in slot 4. RT SW GG. This means G can move ruling out (A), R can move ruling out (C), and T can move ruling out (D). However, you'll notice that W is in slot 4 in both. Given that there are no other possible hypotheticals that work with all the rules PLUS S must be in slot 3, (E) is correct.
_ _ _ _ _ _
1 2 3
T G T G T G
S R
______________
R S W T GG
GG R S WT
GG R T SW
RT S W GG

Question 5 puts G in slot 3, which following Rule 1 means it dominates the 2 o'clock hour. _ _ GG _ _ So test each answer against the rules.

(A) puts R in 2. T cannot be in slot 1 (rule 2), nor can S (rule 3), nor can W (rule 4), so R cannot be in 2.

(B) puts R last, which is not possible by rule 3.

(C) put S in 4th position, allowing R to be ahead as per rule 3, and T to be ahead of W as needed for rule 4. This is the correct answer.

(D) puts T in 4th, which is at the top of the hour and violates rule 2.

(E) puts W in 2nd, which would necessarily put it before T, which violates both rule 2 and the hypothetical of having G third.

Add RT GG SW to the diagram and move on.
_ _ _ _ _ _
1 2 3
T G T G T G
S R
______________
R S W T GG
GG R S WT
GG R T SW
RT S W GG
RT GG S W

The hypotheticals you've already established rule out (C) and (D) immediately as being possible. Then looking at the third hypothetical, there is no reason in the rules that you could not reverse W and S, making (E) possible. In the fourth hypothetical, there's nothing that would prevent reversing S and W again, making (A) possible.

There are no hypotheticals that place W immediately before R, so through process of elimination, (B) is correct. Rule 1 is the primary reason why W cannot immediately precede R because G starting at the top of the hour forces the half hour shows into two blocks. If W is ahead of T, it must be [WT], and R must be before S. Placing W immediately before R would either put R before S or W before T, both of which would break the hypothetical.

Question 7 asks you to identify the rule that could substitute for G showing only at the top of the hour. Your established hypotheticals can help determine if these work or not, and you can immediately eliminate (B) because you have an example of it not working.

(A) If R were first then G could be second at 1:30, S third and WT fourth and fifth, so it breaks down.

(B) we already eliminated with the hypotheticals.

(C) works.

(D) doesn't constrain things enough, because G could be shown second or fourth, and this rule would have no impact.

(E) This would allow for WT GG RS or WT RG GS, which doesn't work as the original rule.

So (C) is the only answer that works as the original rule worked.

Hope that helps. Let me know if anything needs further clarification.

Jaimee on October 3, 2018

About you explanation of question 1, you eliminate A because you say Terry is not on a half hour mark, but it is. It's actually on the same half hour mark as the correct answer, B. I'm reading through this explanation and it's making absolutely no sense. I feel like some parts are missing. Can you please explain why B is the correct answer and not A?

Mehran on October 16, 2018

@Jaimee-Salgado that is not correct. In (A), T would be starting at 3pm, which violates rule 2.

Since G is an hour long, I will write as GG.

(A)

1 G G
2 R W
3 T S

In (B), T starts at 2:30pm, which satisfies rule 2.

(B)

1 R S
2 W T
3 G G

Hope that helps! Please let us know if you have any other questions.