Question

A doctor must schedule nine patients—L, M, O, P, R, S, T, V, and X—during a given week, Monday through Sunday. At least one patient must be scheduled for each day, and the schedule must observe the following constraints:

M and S must be scheduled for the same day.
On the day P is scheduled, P must be the only patient scheduled to see the doctor.
Exactly one patient is scheduled for Wednesday.
T cannot be scheduled for Thursday.
If P is scheduled for Monday, then V and X must be scheduled for Saturday.
R is not scheduled for Thursday unless L is scheduled for Monday.

If L is scheduled for Monday, which one of the following must be true?
(A) R is scheduled for Thursday.
(B) V is scheduled for Saturday.
(C) S is scheduled for Saturday.
(D) P is not scheduled for Monday.
(E) V is not scheduled for Monday.

Which one of the following statements about the doctor's schedule must be true?
(A) The maximum number of patients scheduled for Monday is one.
(B) The maximum number of patients scheduled for Tuesday is two.
(C) The maximum number of patients scheduled for Friday is three.
(D) The minimum number of patients scheduled for Saturday is two.
(E) The minimum number of patients scheduled for Sunday is two.

Answer 1

If L is scheduled for Monday, R must be scheduled for Thursday. The maximum number of patients for Tuesday can be two, and the minimum number of patients scheduled for Saturday is two, provided P is scheduled for Monday.

Step-by-step explanation:

The logic puzzle presented involves scheduling patients with specific constraints. For the first part of the question, if L is scheduled for Monday, based on the constraints provided, we can analyze the options. Since R is not scheduled for Thursday unless L is scheduled for Monday, and in this case, L is indeed scheduled for Monday, option (A) R is scheduled for Thursday, must be true.

Concerning the second part of the question, considering that there are nine patients and seven days, and with the constraint that P must be the only patient scheduled on the day they are seen, the maximum number of patients on any day except the day P is seen could be two, since 8 patients must be spread over six days (at least one patient per day). Therefore, option (B) The maximum number of patients scheduled for Tuesday is two, must be true.

Lastly, the minimum number of patients scheduled for Saturday can be determined. Given that P is scheduled for Monday means V and X must be scheduled for Saturday, so the minimum number of patients for Saturday is two, making option (D) The minimum number of patients scheduled for Saturday is two, the correct statement.