There is exactly one possible order in which the cities are used if which one of the following is true?

Luke on February 14 at 01:17PM

Options D & E

I'm not understanding the difference between options D&E, it seems like either forces you into the same one sequence, how do you differentiate them?

1 Reply

Shunhe on February 14 at 03:44PM

Hi @Luke,

Thanks for the question! First, let’s take a look at answer (D). (D) tells us that V is used in the first slot.

V _ _ _ _ _

Well, based on rule 2, we know W must be in the second slot, and based on rule 4, we know that L must be in the fourth slow.

V W _ L _ _

But now, based on rule 1, we know that T is in the third slot.

V W T L _ _

Finally, based on rule 3, we know that M is in the last slot, leaving N for the second-to-last slot.

V W T L N M

And so we know that (D) is right because it leaves open only this order. Now let’s take a look at (E). Let’s put W in the second slot.

_ W _ _ _ _

Now, notice that one possibility is the slot we just derived, so we know there’s at least that possibility. But based on rule 2, V can go before or after W. Let’s try putting V after W and see if we can make any boards that are consistent with the rules.

_ W V _ _ _

Well, we know that V and L are separated by two, so L goes in the last slot.

_ W V _ _ L

We also know that M and T differ by 2, which means one of them has to be first, and the other fourth. Then we can put N in fifth. So we can actually make another two game boards at least:

M W V T N L

T W V M N L

And since these are consistent with the rules, there’s more than one possible order with (E), and so (E) is wrong. Hope this helps! Feel free to ask any other questions that you might have.