# Mollie must be assigned to 1922 if which one of the following is true?

claire_crites on May 29, 2019

Question

I really struggled with this game. How does Yoshio being assigned to 1921 ensure that Mollie is in 1922? The two don't seem to be related. thanks!

Replies

Ravi on May 30, 2019

@claire_crites,

Great question. Let's look at the setup first.

We have a 4-slot game board with 2 pieces that are out

_ _ _ _ | _ _

Our pieces are L, M, O, R, T, and Y.

Rule 1 says L or T has to be in 1923

_ _ L/T _ | _ _

Rule 2 says if M is in, she's in 1921 or 1922

M in - >21 or 22

Rule 3 says if T is in, then R is in.

T - >R

Rule 4 says if R is in, then O has to be in in the year before R

R - >OR

We can also combine rules 3 and 4 together

T - >R - >O and OR

This is an important inference because if we try to put O out, that
means both R and T would also have to go out. However, we only have 2
spots in the out group. so this means that O must go in.

If R goes out, we know that T goes out, so this is a good place to
split up the game board.

_ _ L/T _ | _ _

In this game board, we're putting R in, so OR have to go together. The
only spot for them to do so is in 1 and 2.

O R L/T _ | _ _

This also means that M is out since 1921 and 1922 are occupied by O and R.

O R L/T _ | M _

Now let's look at our other board.

_ _ L/T _ | _ R

If R is out, then T is out.

_ _ L _ | T R

Now let's look at the question. Mollie must be assigned to 1922 if
which one of the following is true?

We know M is in the game, so we're only concerned with our second board.

_ _ L _ | T R

(A) Louis is assigned to 1924.

The only scenario in which this occurs is the first board, and M is
out in that board, so this answer is automatically out.

(B) Onyx is assigned to 1921.

(B) doesn't work because in our first game board, we have O in 1921 and M out.

O R L/T _ | M _

(C) Onyx is assigned to 1924.

If O is in 1924, M could still be in 1921 or 1922 in our second game
board, so (C) is out.

(D) Tiffany is assigned to 1923.

The first game board is the only board where T could be in 1923, and
in that board, M is out, so (D) is out.

(E) Yoshio is assigned to 1921.

Our first board has O in 1921, so we're looking at the second game board.

_ _ L _ | T R

If Y is in 1921, then M has to go in 1922 because T and R have already
filled up the out group and we know that if M is in, it has to go in
1921 or 1922. Since 1921 is full, it has to be in 1922. Thus, (E) is

Does this make sense? Let us know if you have any more questions!

ElliottF on July 31, 2020

Maybe I am just missing something obvious but why is (b) also not possible? It would seem any variable that doesn't have an extra rule against it taking 1921 would force M into 1922? Why does it have to be Y vs O? Am I missing a rule that say O can't go in spot 1 or 4 or hence an ordering of:

OMLY or YMLO. Both seem valid ?

shunhe on August 4, 2020

Hi @ElliottF,

Thanks for the question! So the question here is going to be about what, if true, will force Mollie to be in 1922. Remember, the second rule only tells us that IF Mollie is in the project, she has to be in 1921 or 1922. So someone could be in 1921, and Mollie’s just not in the project. And in that case, she wouldn’t have to be assigned to 1922.

So let’s look at (B). It tells us that O is assigned to 1921. So let’s put O there, and just not put M in the game! Then we could have something like

ORTY

And that doesn’t violate any rules, and also doesn’t assign M to 1922. So O can be in 1921 and M not in 1922, so (B) is wrong. The answer choice has to both force M to be in the game and force M to be in 1922 instead of 1921, and that’s what (E) does.

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