Exam Scheduling 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 the week from Monday to Sunday. We are given several conditions and need to find out which person has their exam on Wednesday.

Exam Schedule Clues Analysis

Let's break down the information provided:

• Fixed Point: Q's exam is on Friday.

  Current Schedule: Mon: ?, Tue: ?, Wed: ?, Thu: ?, Fri: Q, Sat: ?, Sun: ?

• R and T Constraint: Exactly 3 people have exams between R and T. Also, neither R nor T has an exam on Sunday. This means there must be 3 days separating R and T. Given the 7-day week (Mon-Sun), the possible day pairs for (R, T) or (T, R) are:
  • Monday and Friday (Tue, Wed, Thu are between)
  • Tuesday and Saturday (Wed, Thu, Fri are between)
  We exclude pairs involving Sunday as per the constraint.
• Consecutive Pair 1: P has an exam immediately after U. This means they form a block: UP.
• Consecutive Pair 2: V has an exam immediately before T. This means they form a block: VT.

Schedule Deduction Steps

We will now combine these clues to build the schedule:

1. Integrating VT and Q: The block VT must exist. Since Q is on Friday, T cannot be on Saturday (V would be on Friday), nor can T be on Thursday if V is on Wednesday and Q is Friday, as this leaves fewer slots. Let's test the possible R and T positions derived from Clue 2:
   • Case 1: R=Mon, T=Fri. This conflicts with Q being on Friday. So, this case is impossible.
   • Case 2: R=Tue, T=Sat. The days between R and T are Wed, Thu, Fri. Q is on Friday. Clue 4 states VT. For T=Sat, V must be on Friday. This conflicts with Q being on Friday. So, this case is impossible.
   • Case 3: T=Mon, R=Fri. This conflicts with Q being on Friday. So, this case is impossible.
   • Case 4: T=Tue, R=Sat. The days between R and T are Wed, Thu, Fri. Q is on Friday. Clue 4 states VT. For T=Tue, V must be on Monday. This fits perfectly.
     • Current Schedule Update: Mon: V, Tue: T, Wed: ?, Thu: ?, Fri: Q, Sat: R, Sun: ?
2. Placing the UP block: The remaining people are U, P, and S. The remaining days are Wednesday, Thursday, and Sunday. Clue 3 requires the UP block. The only consecutive days available are Wednesday and Thursday.
   • Therefore, U must have the exam on Wednesday, and P must have the exam on Thursday.
   • Updated Schedule: Mon: V, Tue: T, Wed: U, Thu: P, Fri: Q, Sat: R, Sun: ?
3. Final Placement: The only person left is S, and the only day left is Sunday.
   • Final Schedule: Mon: V, Tue: T, Wed: U, Thu: P, Fri: Q, Sat: R, Sun: S.
4. Verification: Let's check if the final schedule satisfies all original conditions:
   • Q on Friday: Yes.
   • 3 people between R (Sat) and T (Tue): Wed, Thu, Fri (3 people). Yes.
   • R/T not on Sunday: Yes (T=Tue, R=Sat).
   • P immediately after U: Yes (U=Wed, P=Thu).
   • V immediately before T: Yes (V=Mon, T=Tue).
   All conditions are met.

Wednesday Exam Determination

Based on the confirmed schedule:

The person scheduled for the exam on Wednesday is U.