Q20

[karincao9710]

Ok, this question tripped me up a bit the first time, so I thought I would provide an explanation with the answer here in case anyone was looking for it. What is the minimum number of solos which Wayne performs a traditional piece...Now, I did an initial frame around rule 3 (the fourth solo is either Wayne-Traditional or Zara- Modern). So, the question is what is the minimum # of solos Wayne could perform traditional piece. Since none of the rules definitively puts Wayne-Traditional as one of the solos, let's test out a scenario where Wayne could perform no traditional pieces.

In that scenario...
Rule 3 would put Zara Modern as the fourth piece

_ _ T M _
_ _ _ Z _

Then we would know that the second piece has to be traditional because of rule 2, exactly two of the traditional pieces are performed consecutively.

We also know then that the first piece has to be Wayne-Modern because the second piece is traditional and no traditional pieces are performed until Wayne performs at least one modern (rule 5).

MTTM_
W_ _ Z _

So since we are working within the scenario that Wayne doesn't perform a traditional solo, pianists for solos 2 and 3 have to be Zara.

MTTM_
WZZZ_


Finally, we have to pay attention to the rule that the pianists for the second and fifth solos cannot be the same (rule 4). Since the second solo is played by Zara, the last solo has to be played by Wayne. Since we don't want Wayne playing a traditional piece, we have to put Wayne-Modern for solo #5 and that works. Wayne can perform zero traditional pieces.

MTTMM
WZZZW

[ohthatpatrick]

EXCELLENT explanation, thanks!