Exam Schedule Logic Puzzle

This problem involves determining the order of exams for 7 people (P, Q, R, S, T, U, V) across a week (Monday to Sunday) based on specific conditions.

Analyzing Exam Schedule Constraints

• Constraint 1: 5 people between V and T. This indicates V and T are at the week's ends (Day 1 and Day 7).
• Constraint 2: 2 people between R and T.
• Constraint 3: Q's exam is immediately after R's (QR sequence).
• Constraint 4: S's exam is immediately before P's (SP sequence), and S's exam is after T's.

Determining the Correct Exam Order

We test the two possible arrangements for V and T:

1. Scenario 1: V on Monday (Day 1), T on Sunday (Day 7)
   • Initial Setup: V _ _ _ _ _ T
   • Applying Constraint 2 (2 between R and T): R must be on Day 4. Setup: V _ _ R _ _ T.
   • Applying Constraint 3 (QR): Q must be on Day 5. Setup: V _ _ R Q _ T.
   • Applying Constraint 4 (S after T): S must be after Day 7, which is impossible. This scenario is invalid.
2. Scenario 2: T on Monday (Day 1), V on Sunday (Day 7)
   • Initial Setup: T _ _ _ _ _ V.
   • Applying Constraint 2 (2 between R and T): R must be on Day 4. Setup: T _ _ R _ _ V.
   • Applying Constraint 3 (QR): Q must be on Day 5. Setup: T _ _ R Q _ V.
   • Applying Constraint 4 (SP sequence, S after T): The remaining slots are Day 2, Day 3, and Day 6. The SP sequence must fit contiguously. The only available adjacent slots are Day 2 and Day 3. Setup: T S P R Q _ V.
   • The only remaining person is U, and the only remaining slot is Day 6.
   • Final Schedule: Monday(T), Tuesday(S), Wednesday(P), Thursday(R), Friday(Q), Saturday(U), Sunday(V).

Calculating People Between P and U

From the final schedule:

• P's exam is on Wednesday (Day 3).
• U's exam is on Saturday (Day 6).

The exams scheduled between P (Day 3) and U (Day 6) are on Day 4 and Day 5.

These correspond to R (Day 4) and Q (Day 5).

Therefore, there are Two people with exams between P and U.