# If the scythe is in case 3, which one of the following must be true?

Tyler808 on July 7, 2022

Hard question

This is one of the questions where, I set it up, each answer correlated with my set up. These type of questions is what eats my time. Help. This fricken frustrating.

Emil-Kunkin on September 29, 2022

Hi Tyler, There is a great explanation of the question that I will pass in below from a few years ago. However, I am interested in how you approach this question in general. Usually, a must be true question will be something that we are able to make a deduction about that forces it to be true. Here, it is quite difficult to prove why C must be true, so we could use our plan B: proving that the four other answer choices could be false.

I think that when we do that, we should not start with a setup, but rather, start with an answer choice. That is, for A, we would try to start a scenario where G is not in 4, perhaps by putting it in two, and so on.

Copying in Victoria's old post now.

The correct answer for the question you've attached your post to is (C). I'm happy to outline the setup for the game and demonstrate why (C) is the correct answer for this question.

If you meant to ask about another question in this game, hopefully the setup helps you to figure it out! If not, drop us a comment on the question you're still having trouble understanding.

We know that a museum will display seven artifacts in seven individual cases - G, H, J, M, N, P, and S.

The cases are numbered 1 through 7 and will be arranged in a circle i.e. 1 is next to 7.

As I'm typing this, I'm going to put them in a line, but we'll need to remember that 1 is next to 7.

1: _ 2: _ 3: _ 4: _ 5: _ 6: _ 7: _

Now let's go through the conditions.

Rule 1 - Either H or J is in case 7.

1: _ 2: _ 3: _ 4: _ 5: _ 6: _ 7: H/J

Rule 2 - N is in a lower-numbered case than M.

As case 7 is already filled, this means that N cannot be in case 6 and M cannot be in case 1.

Rule 3 - H is next to M

There are two possibilities here:

(1) If H is in case 7, then M must be in case 6. While we know that 1 is also next to 7, Rule 2 tells us that N must be in a lower-numbered case than M. Therefore, M cannot be in case 1.

(2) If H is not in case 7, then the only condition is that H cannot be in case 1. This is because M would have to be in case 2 and this would leave no space for N to be in a lower-numbered case.

Rule 4 - P is not next to S.

Rule 5 - Neither P nor S is next to J

Overall, there are two broad scenarios:

(1) H is in case 7

1: J/P/S 2: G/N 3: P/S/J 4: N/G 5: S/J/P 6: M 7: H

We outlined above that, if H is in case 7, then M must be in case 6. We know that neither P nor S is next to J. We also know that P and S cannot be next to each other. Therefore, J/P/S must be in cases 1, 3, and 5 so they are not next to each other.

G/N must therefore be in cases 2 and 4. The only condition restricting their position is that N must be lower than M and this would be true in either case.

(2) J is in case 7

1: N 2: P/S 3: H/M 4: M/H 5: G 6: S/P 7: J

P/S cannot be in case 1 or case 6 as these are both next to case 7.

We also know that H and M must be next to one another. Therefore, there must be two spaces between S/P and P/S.

We also know that N must be lower than M. Therefore, N must be in case 1 and G must be in case 5.

Now that we've gone through the conditions and diagrammed a couple possible scenarios, let's address the question. The question stem places S in case 3 and asks which one of the answer choices must be true based on this.

1: _ 2: _ 3: S 4: _ 5: _ 6: _ 7: H/J

This is most similar to scenario 1 that we diagrammed above so let's see which answer choices we can eliminate based on that.

We can eliminate answer choices (A) and (D) as G/N could be in either cases 2 and 4 or cases 4 and 2, respectively.

We can also eliminate answer choices (B) and (E) as J/P could be in either cases 1 and 5 or cases 5 and 1, respectively.

Therefore, the correct answer is (C) - M must be in case 6.