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

Irina on November 25, 2019

@suzanne,

Thanks for letting us know and we are terribly sorry to hear that you are experiencing technical issues.

Please direct any support related issues to our support staff by tapping "support" from the left menu or by calling 855.483.7862 ext. 2 Monday-Friday 9am-6pm PT.

Our support channels are a much faster way to resolve these type of issues.

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.