# If Tyrone plays in the fourth game, then which one of the following could be true?

Lizzie-Annerino on June 2, 2019

Confused

I felt like all of the answer choices could have been true. Could you diagram one or two of them to show why they couldn't have been true?

Ravi on June 3, 2019

@Lizzie-Annerino,

Happy to help.

Before we look at the question, let's make sure our game setup is good.

We have 4 chess games and 6 players, so we know there will be some
repeats. The pieces are L, N, O, P, S, and T.

_ _ _ _
_ _ _ _

We know T isn't in 1 or 3, so T has to be in 2 or 4. The two slots in
both 2 and 4 are interchangeable because the slots represent the
players in the game.

L plays in 4

_ _ _ L
_ _ _ _

We know that N is only in one game and it isn't with P

NP not together and N doesn't repeat

S plays in 2 games, 1 just before and just after O plays

SOS

We can split the game into two boards, putting the SOS next to L and
then another where SOS overlaps with L

SOSL
_ _ _ _

_ _ _ L
_ S O S

In the second board, T must go in 2 because 4 is totally occupied

_ T _ L
_ S O S

We know N and P can't be together, so they have to split 1 and 3

N T P L
_S O S

or

P T N L
_ S O S

The other position has to be L since it's the only player available to
fill in the spot in 1

P T N L
L S O S

Since we know N and O don't repeat, we know that either L, P, or T
must repeat so that we fill out all 8 slots.

In looking at the top board, it's still very open, so we just need to
keep in mind the rules for it.

SOSL
_ _ _ _

The question tells us that T is in 4. This means we're looking at the
first game board since T is in 2 in our second one.

SOSL
_ _ _T

With (A), N could definitely be in 2. We could put P in 3 and L in 1.

(B) is wrong because there's only 1 O allowed, and it's already occupying 2.

(C) is wrong because there are 2 S pieces on our board already and
they're in 1 and 3.

(D) is wrong because T is with L, so N can't be with L

(E) is wrong because T is with L, so P can't be with L

SOSL
_ _ _T

Hope this helps. Let us know if you have any more questions!