# What is the minimum number of solos in which Wayne performs a traditional piece?

suzanne on November 25, 2019

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Hello video not working can we please get a game setup? Thanks.

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Irina on November 25, 2019

@suzanne,

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Please see below for the setup:

During the recital two pianists - W & Z - will perform five solos total, each will either be a modern piece or a traditional piece - M or T.

W/Z __ __. __. __. __
M/T __. __. __. __. __
1. 2. 3. 4. 5

The following rules apply:

(1) 3d solo is a traditional piece.

W/Z __ __. __. __. __
M/T __. __. T. __. __
1. 2. 3. 4. 5

(2) Exactly two of the traditional pieces are performed consecutively.

This rule tells us that we must have exactly one TT sequence.

(3) In the fourth solo, either W performs a traditional piece or Z performs a modern piece.

W/Z __ __. __. W/Z. __
M/T __. __. T T/M __
1. 2. 3. 4. 5

Let's consider both of these scenarios. If W performs a traditional piece as the fourth solo, #3 & #4 are both consecutive traditional solos, meaning #5 and #2 must be modern pieces per rule (2).

__ M T T M

If #4 is a modern piece performed by Z, then the only possible placement for the TT sequence is #2 and #3, and we can infer that #1 must be a modern piece in this scenario.

M T T M _

To put both possible scenarios for the type of piece together:
(1) ? M T T M
(2) M T T M ?

(4) The pianist who performs the second solo does not perform the fifth solo.

2 -> ~5
5-> ~2

This rule tells us that solo #2 and #5 must be performed by different pianists, thus if Z performs 2, W performs 5 and vice versa.

W/Z __ W/Z __. W/Z. Z/W
M/T __. __. T T/M __
1. 2. 3. 4. 5

(5) No traditional piece is performed until W performs at least one modern piece.
Since we know that #3 is a traditional piece, we know that W must perform a modern piece either for the first solo, second solo or for both of them.

W/Z __ W/Z __. W/Z. Z/W
M/T __. __. T T/M __
1. 2. 3. 4. 5
/W. /W
/M. /M
If W performs a modern piece for the second solo, we can infer that Z must perform the fifth solo.

Combined with our inferences above for the possible scenarios of the type of pieces:

? MTTM
MTTM?

we can conclude that the first piece must be modern, thus resulting in the two final scenarios:

(1) MMTTM
(2)MTTM M/T

Let's consider if we can make any inferences regarding the performers for each of these scenarios:

Scenario 1:
We know that W performs the fourth piece per rule (3), and we can infer that W must perform either piece #1 or #2 or both per rule (5).
W
M M T T M
/W /W

If W performs the second piece, then Z must perform the fifth piece per rule (4), and if W performs the first piece and Z performs the second piece, W must perform the fifth piece, resulting in the following 3 scenarios:

W W ? W Z
W Z ? W Z
Z W ? W W

Scenario 2:
We know that Z performs the fourth piece per rule (3), and can infer that the first modern piece must be performed by W per rule (5).

W Z
MTTM?

The rest of the pieces could be performed by either W or Z as long as pieces 2 and 5 are performed by different pianists.

The question asks us which of the following is the minimum number of solos in which Wayne performs a traditional piece?

Let's look at both of our scenarios above - W is not required to perform any traditional solos under scenario 2 thus we can conclude that the minimum number of solos in which Wayne performs a traditional piece is 0 - answer choice (A).

Let me know if this makes sense and if you have any other questions.