Exam Schedule Logic Puzzle

This problem requires us to determine the exam schedule for seven individuals (P, Q, R, S, T, U, and V) across the days of a week, from Monday to Sunday. We need to use the given conditions to establish the correct order and then count the number of people scheduled between Q and P.

Deduction of Weekly Exam Schedule

Let's break down the conditions to figure out the schedule day by day:

1. Condition 1: R's Exam Day

   We are explicitly told that R has an exam on Tuesday.

   • Monday:
   • Tuesday: R
   • Wednesday:
   • Thursday:
   • Friday:
   • Saturday:
   • Sunday:
2. Condition 2: U and R's Exam Interval

   The condition states that there are exactly two people scheduled between U and R.

   Since R is on Tuesday, U cannot be on Monday. If U were on Monday, there would be three days (Monday, Wednesday, Thursday) between U and R (Tuesday), violating the condition. Thus, U must be scheduled after R.

   The arrangement must be R, [Person 1], [Person 2], U. With R on Tuesday, this sequence means U must be on Friday (Tuesday + 3 days = Friday). The exams on Wednesday and Thursday fall between R and U.

   • Monday:
   • Tuesday: R
   • Wednesday:
   • Thursday:
   • Friday: U
   • Saturday:
   • Sunday:
3. Condition 3: Q and V's Exam Proximity and Constraint

   We know that Q's exam is scheduled immediately before V (a QV block). Also, Q's exam is not on Wednesday.

   Let's examine the possible days for the QV block:

   • Monday-Tuesday: Impossible, as R is on Tuesday.
   • Tuesday-Wednesday: Impossible, as R is on Tuesday.
   • Wednesday-Thursday: Impossible, as Q cannot be on Wednesday.
   • Thursday-Friday: Impossible, as U is on Friday.
   • Friday-Saturday: Impossible, as U is on Friday.
   • Saturday-Sunday: This is the only remaining valid slot.

   Therefore, Q is scheduled for Saturday, and V is scheduled for Sunday.

   • Monday:
   • Tuesday: R
   • Wednesday:
   • Thursday:
   • Friday: U
   • Saturday: Q
   • Sunday: V
4. Condition 4: S and T's Exam Proximity

   S has an exam scheduled immediately before T (an ST block).

   The available days for scheduling are Monday, Wednesday, and Thursday.

   The only consecutive days available for the ST block are Wednesday and Thursday.

   • Monday:
   • Tuesday: R
   • Wednesday: S
   • Thursday: T
   • Friday: U
   • Saturday: Q
   • Sunday: V
5. Condition 5: Placing P

   The only person remaining is P, and the only day left is Monday.

   So, P's exam is scheduled for Monday.

Final Exam Schedule Overview

The determined schedule for all seven people is as follows:

Finding Number of People Between Q and P

The final step is to count the number of people whose exams fall between P's exam (Monday) and Q's exam (Saturday).

Looking at the schedule:

• P is scheduled on Monday.
• Q is scheduled on Saturday.

The days situated between Monday and Saturday are Tuesday, Wednesday, Thursday, and Friday.

The individuals scheduled on these days are R, S, T, and U.

By counting these individuals, we find that there are Four people with exams scheduled between Q and P.