# Which one of the following could be the order of the nurses' sessions, from first to last?

SarahA on May 14, 2019

Game Setup

Looks like we need a Game Setup here, or perhaps at least a diagram? Thank you :)

Replies

Ravi on May 15, 2019

@msaber,

Happy to help.

This is a 7-item sequencing game.

_ _ _ _ _ _ _
1 3 5 7

We have 7 game pieces:

F G H
J K L M

Now, let's take a look at the rules.

Rule 1 says at least 2 nurse session go between H and M

1) H_ _ M or M _ _ H (at least 2 in between)

Rule 2 says G goes the day before K

2) GK

Rule 3 says J goes after M

3) M - J

Rule 4 says F is before K but after L

4) L - F - K

We can combine rule 2 and rule 4 because they have overlapping pieces:

L - F - GK

Rule 5 says L can't be in 2

5) L not in 2

Notice how each piece is mentioned in at least 1 rule, so there aren't
any floaters.

What inferences can we make? Let's Look at L because it's a leader and
has a lot of things after it, and it can't go in 2.

We know L can't go in 5, 6, or 7 because it has at least 3 pieces
after it. Based on what we see so far, L looks like it could go into
1, 3, or 4, but we don't know for sure since there are also a bunch of
other rules.

Let's see what happens if we put L in 4.

If L is in 4, then we know F, G, and K need to go in 5, 6, and 7.
However, we have a problem now. Remember rule 1? Well, with L in 4, H
and M don't have at least 2 spots between them, which they need. This
means L can't be in 4. So now L just has 2 possible options (1 and 3).
Let's test L in 3 now.

If L is in 3, F, G, and K have to go after, but there's still a free
spot for M or H to go in, which means that H and M can be separated by
at least 2 spots.

Let's make 2 game boards: one with L in 1, and one with L in 3.

L _ _ _ _ _ _

_ _ L _ _ _ _

In looking at the L in 3 board, we know H and M have to have at least
2 pieces between them and M has to go before J. However, we have a
problem if we put J after L with F, G, and K. If J is back there, then
H and M have to go in 1 and 2, so that doesn't work. So J has to be in
1 or 2, and we know J is a follower, so J must go in 2. We also know M
has to go before J, so M is in 1.

M J L _ _ _ _

Now H goes after L with F, G, and K. It can go anywhere there s long
as we satisfy the L - F - GK rule.

Now, let's look at the L in 1 board.

The L can't be in 2 rule is irrelevant since we have L in 1, and we
also know that because L is before everyone else, then the L - F - GK
rule reduces to F - GK.

L _ _ _ _ _ _

This board is very open-ended, so we just need to keep in mind the
rules of the game when looking at it.

Armed with these scenarios, we're well equipped to answer the
questions in this game.

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

SarahA on May 15, 2019

Great explanation thank you, Ravi!