# Which one of the following speakers CANNOT lecture at 1:00?

Rachelsusany on January 4, 2020

Why no explanation for these

Why is there no explanations

AndreaK on January 5, 2020

Hi @Rachelsusany

Letâ€™s see if I can help you out with this one. I think this is a good game for scenarios.

We have four rules. I chose rule 1 in combination with rule 4 to break the game down with, because the two working together restrict the game. Starting with rule 1, there are only two places J can goâ€”either at 1 oâ€™clock on T of F.

Scenario 1:
1 2 3
T J
F

Scenario 2:
1 2 3
T
F J

Now, letâ€™s think about how rule 4 plays in with rule 1. Rule four further restricts a 1 oâ€™clock spot. Because J is at 1 on Friday in scenario 2, we know L canâ€™t be there. So, we therefore know L is not on Friday. If L is not on Friday, then L must be on Thursday. Knowing L is on Thursday kicks rule 3 into play, with then means Ota is on Friday. Knowing Ota is on Friday means the Friday slots are almost filled. Only one of three slots remains, either at 2 or 3 oâ€™clock. Keep in mind we donâ€™t know when on Friday Ota goes yetâ€”just that she is on Friday. However, we donâ€™t have to know what time she goes on Friday to make another key deduction here. The fact that there is only one spot remaining in the Friday category limits our game further through rule 2, M and N lecture on the same day as each other. Since there is only one spot left on Friday, but M and N must go together, that means neither can go on Friday since there is not enough room for both of them. So, M and N must go at some point on Thursday, which leaves our last remaining player, K, to fill that last slot sometime on Friday.

Scenario 2:
1 2 3
T L/M/N (LMN can each be in any time slot on this day,)
F J O/K (O and K can both be at either 2 or 3, but J must be at 1)

Note: The slashes connecting letters mean they are interchangeable among the time slots on that day. Letters not connected by a slash are committed to the slot they are seen in.

Rule 4 made scenario 2 fill out quickly. Now, letâ€™s see what we can do to fill out scenario 1.

Scenario 1:
1 2 3
T J
F

Before, we used rule 4 to start scenario 2. However, since here L is neither ruled out of or committed to the Friday at 1 slot, I would look elsewhere to restrict the game. My next thought is considering crowding. Rule 2 says M and N have to lecture the same day as each other. However, rule 3 says O and L canâ€™t lecture on the same day as each other. So, that means either O or L has to be lecturing with our M and N pair, because there are only three slots on each day and O and L canâ€™t both be on the same day. That also means, then, that M and N canâ€™t be on Thursday with J. That would force L and O together. So, M and N must be on Friday with either O or L.

Letâ€™s think about how that restricts the game. There are two ways that could play out.

1 2 3
T J L/K (L and K can both be at either 2 or 3, but J must stay at 1)
F M/N/O (these can be in any order on this day)

- and -

1 2 3
T J O/K (O and K can both be at either 2 or 3, but J must stay in 1)
F L M/N (M and N can both be at either 2 or 3, but L must stay in 1)

Take note in the second option, because L is in Friday, it must be in that 1 oâ€™clock spot because of rule 4. So, that makes this second option slightly more restricted than the one above it.

Personally, I would use the two possible options for scenario one as two separate scenarios, for a total of three scenarios to help me though this game.

Now, letâ€™s hop into the question.

Which one of the following speakers cannot lecture at 1?

I recommend looking at all the 1 oâ€™clock slots across our scenarios before looking at the answer choices. Do you noticed one player that canâ€™t ever have that 1 oâ€™clock slot?

Scenario 2:
1 2 3
T L/M/N (LMN can each be in any time slot on this day)
F J O/K (O and K can both be at either 2 or 3)

Scenario 1, Option 1:
1 2 3
T J L/K (L and K can both be at either 2 or 3)
F M/N/O (these in any order on this day)

Scenario 1, Option 2:

1 2 3
T J O/K (O and K can both be at either 2 or 3)
F L M/N (M and N can both be at either 2 or 3)

Remember that the slashes between two players mean that those players can switch between time slots. Players without slashes connecting them to other players are glued to their time slot. We can see J and L are glued to their time slots in two of our scenarios. We can also see from Scenario 1, Option 1 that M, N and O can alternate and each potentially fill that 1 pm slot. So, the only odd one out I see is K, who is constrained to slots at 2 or 3 pm in every option.

That gets us right to answer choice A, K. I hope this set up helps you understand this game and question better! Feel free to follow up if you have any more questions.