If R's speech is immediately after S's speech and immediately before K's speech, then which one of the following coul...

Irina on September 30, 2019

@Ryan-Mahabir,

Let's first look at the setup for this game. This game requires us to determine the order of six student speeches - H J K R S T

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

The following rules apply:

(1) The speeches delivered by H J K no matter what their order is relative to each other cannot form a sequence of three consecutive speeches.

This rule tells us that we cannot have HJK or HKJ or JKH or JHK or KJH or KHJ sequence, but it leaves open the possibility of only two of these speeches being consecutive, e.g. HJ or KH.

(2) The speeches delivered by R S T no matter what their order is relative to each other cannot form a sequence of three consecutive speeches.

This rule similarly tells us we cannot have any consecutive sequences involving these three letters - no RST, RTS, STR, SRT, TRS, TSR.

(4) H speech must be earlier than S speech.

This rule allows us to infer that H cannot be #6, and S cannot be #1.

__ __ __ __ __ __
1 2 3 4 5 6
~S ~H

(5) J speech can be neither first nor sixth.

We can infer that J must be #2, 3, 4, or 5.

/J /J /J /J
__ __ __ __ __ __
1 2 3 4 5 6
~S ~J
~J ~H

(6) T's speech can be neither immediately before nor immediately after J speech.

This rule tells us we can have neither TJ nor JT sequence.

The question asks us R speech is immediately after S speech and immediately before K speech, which of the following could be true?

Let's consider the order in this case:

What could be the possible placement of the SRK block?
We know that per rule (4), S cannot be #1, let's consider if SRK could be 2,3,4 or 3,4,5, or 4,5,6.

If SRK is 2,3,4, then H must be #1 per rule (4), J must be #5 per rule (5), and T must be #6, which is impossible as it would violate rule (6) placing TJ in consecutive slots.

H S R K J T

It is thus impossible for SRK to be in 2,3,4 slots.

If SRK is in 3,4, 5, then H must be #1, J is #2, and T is #6.

H J S R K T

This scenario complies with all the rules and could be true.

If SRK is in 4,5,6, then ss T and J cannot be adjacent to each other per rule (6), and J cannot be #1 per rule (5), J must be #3, T must be #1, and H must be #2:

T H J S R K

This scenario also complies with all the rules. Thus, the only two possible scenarios for this question are:

(1) H J S R K T
(2) T H J S R K

Let's look at the answer choices:

(A) H is immediately before S speech.

HS block is in neither of the two possible scenarios, hence given the rules of this question, HS must be false and could not be true.

(D) K is immediately before T speech.

This is our scenario (1) above, if S R K are in slots 3,4,5, T could be #6. Hence, we can conclude it could be true, and is therefore the correct answer.

Let me know if this makes sense and if you have any further questions.

akosua on March 3, 2021

Hi, I am still confused as to why the answer can not be A. Why don't the possible scenarios include HSJRKT or THSRJK?

Emil-Kunkin on December 1 at 03:25PM

Those would both violate the new condition imposed by this question.