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

bcross on June 18, 2020

Could someone please explain the setup for this game and why B is the correct answer instead of C?

Replies

Victoria on June 18, 2020

Hi @bcross,

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.

Hope this helps! Please let us know if you have any further questions.

Majd on September 3, 2020

Could you explain this question a little more? I was able to put m or h in spots 1 and 2 and then s,n,p,g,j. It doesn't break any of the rules.

Victoria on October 8, 2020

Hi Majd,

Happy to help!

Let's start by going through the rules again.

Rule 1 - either H or J is in case 7
Rule 2 - N is in a lower-numbered case than M
Rule 3 - H is next to M
Rule 4 - P is not next to S
Rule 5 - Neither P nor S is next to J

Now let's go through the set-up you've outlined.

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

This breaks Rule 2 because N (case 4) is in a higher-numbered case than M (case 1 or 2).

But why is answer choice (C) correct?

We know from Rule 1 that M cannot be in case 7 because either H or J is in case 7. We also know from Rule 2 that M cannot be in case 1 because N must be in a lower-numbered case than M. Finally, we know from the question stem that M cannot be in case 3 because S is in case 3.

Therefore, M could possibly be in case 2, 4, 5, or 6. So, let's try each of these out.

Option 1: M is in case 2

The only possible place for N is case 1 because it is the only case lower than case 2. However, this breaks Rule 3 because H cannot be next to M.

N M S _ _ _ _
1 2 3

Option 2: M is in case 4

As S is in case 3, this means that H must be in case 5. This also means that J must be in case 7 because H cannot be in case 7.

We know from Rules 4 and 5 that P is not next to S or J. We can't put P in case 2 because that is next to S. We can't put P in case 6 because that is next to J.

It would seem that the only spot for P is case 1. But wait! The stimulus tells us that the cases are arranged in a circle with case 1 next to case 7. Therefore, no matter where we place P, it breaks either Rule 4 or Rule 5.

_ _ S M H _ J
1 2 3 4 5 6 7

Option 3: M is in case 5

Again, we can see that we'd run into the same problem as above. If we put P in case 2 or 4, it is next to S. If we put P in case 1 or 6, it is next to J.

_ _ S _ M _ J
1 2 3 4 5 6 7

This means that it must be true that M is in case 6. Then we can put P in case 5 and N in case 4 to ensure that we don't run into the same problem as above. This means H would need to be in case 7 and J would need to be in case 1, leaving G to go in case 2.

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

Notice that this meets all of our conditions:

1) H is in case 7
2) N is in case 4 which is lower than case 6 which contains M
3) H is in case 7 which is next to M in case 6
4) P is in case 5 which is not next to S in case 3
5) P is in case 5 and S is in case 3. Neither of these are next to J in case 1.

Hope this helps! Please let us know if you have any further questions.