# If the fifth solo is a traditional piece, then for exactly how many of the solos is the choice of pianist completely ...

on April 21, 2020

thanks!

on April 26, 2020

Hello @kassidee,

I'll start with the basic setup. This is going to be a multi-linear game, with one line for the pianist and one line for the solo type.
P: W Z
S: M T

P: _ _ _ _ _
S: _ _ _ _ _

The third solo is a traditional piece.

P: _ _ _ _ _
S: _ _ T _ _

Exactly two of the traditional pieces are performed consecutively. Think about this rule. "Exactly 2" means we cannot have 3 in a row. So, our TT block must include the one that we already placed in number 3. This gives us two options, and I will make a diagram for each.
1.
P: _ _ _ _ _
S: _ M T T M

2.
P: _ _ _ _ _
S: M T T M _

In the 4th solo, either Wayne performs a traditional piece or Zara performs a modern piece. In Diagram 1, it has to be Wayne. In Diagram 2, it has to be Zara.
1.
P: _ _ _ W _
S: _ M T T M

2.
P: _ _ _ Z _
S: M T T M _

Our next rule gives us P2 ---> not P5 and P5 ---> not P2.

No traditional piece is performed until Wayne performs at least one modern piece. In Diagram 1, we need a modern solo from Wayne in spot 1 or 2, but we don't know which. In Diagram 2, we can conclude that the first solo is a modern piece by Wayne.
1.
P: W _ _ W _
S: M M T T M
or
P: _ W _ W Z
S: M M T T M

2.
P: W _ _ Z _
S: M T T M _

To your question: If the 5th solo is traditional, then for how many solos is the choice of pianist completely determined? First, let's consider which diagram we are using. If the 5th solo is traditional, then it has to be Diagram 2:

2.
P: W _ _ Z _
S: M T T M T

Just by choosing this diagram, we have determined that Wayne performs the 1st solo and Zara performs the 4th. Are there any other soloists completely determined? No. Solos 2, 3, and 5 can be assigned to either soloist, as long as 2 and 5 are not the same. The correct answer is B, only 2 solos have a determined soloist.