# If the pot is in case 2, which one of the following could be true?

Brooke on April 8, 2020

Could someone please explain how the correct answer is D here and not A? Thanks!

Shunhe on April 8, 2020

Hi @BrookeMag,

Thanks for the question! Let’s say we put P in slot 2. Then we can try to map out another couple of possibilities. For example, we know that neither J or S can be in slots 1 or 3, leaving MNHG. There’s a couple of possibilities that we can just sketch out very quickly. Consider:

G P N S H M J

which has P in slot 2, and involves us putting N in slot 3. This forces M and H to occur after N, which means we can put G in slot 1. Recall that H and M have to be adjacent, and H or J has to be the last slot. If we put J in the last slot, we can put H in slot 5 and M in slot 6. This leaves S for slot 4. Note how this doesn’t contradict any of the rules, which means that it’s a possibility, and that’s all we need for a could be true question. We now know that M can be in slot 6 (having noticed that this was one of the answer choices), and so we pick (D) and move on.

Let’s take a look at (A) to see why it’s wrong. Say that P is in 2 and G is in 4.

_ P _ G _ _ _

Now, recall that N is in a lower numbered case than the mask, and the helmet is next to the mask, so N can at latest be in slot 5. Let’s say we put N in slot 5. Then we get (since H would have to be in case 7):

_ P _ G N M H

But now we’re left with S and J, which have to go in slots 1 and 3. But this means that we violate the last two rules about the P being next to J and S.

Let’s say we put N in slot 3. Again, M and H have to follow N. If J also follows N, then S is next to P, violating rule 4. If J does not follow N, then J is in slot 1, violating rule 5.

Let’s say we put N in slot 1. Then M and H follow. But neither M and H can be in slot 3, since they have to be adjacent. This means that S or J are in slot 3. But once again, this violates rule 3/5. Since N can’t be in slots 1, 3, 5, 6, or 7, we know that it’s impossible for P to be in case 2 and G to be in case 4, and (A) is wrong.

Hope this helps! Feel free to ask any other questions that you might have.