Exam Schedule Logic Puzzle Explained

This problem involves determining the exam schedule for seven people (P, Q, R, S, T, U, V) across seven days of the week (Monday to Sunday) based on a set of clues. The goal is to find out how many people have exams scheduled between P and R.

Step 1: Initial Setup and Fixed Positions

We have 7 days and 7 people. Let's list the days:

• Monday
• Tuesday
• Wednesday
• Thursday
• Friday
• Saturday
• Sunday

The first clue states that Q has an exam on Wednesday. We can fix this:

• Monday:
• Tuesday:
• Wednesday: Q
• Thursday:
• Friday:
• Saturday:
• Sunday:

Step 2: Analyzing Relative Positions (Blocks)

We have two blocks of people with consecutive exam days:

• R immediately before S, and V immediately after S. This forms a consecutive block: RSV.
• P immediately before T. This forms a consecutive block: PT.

These blocks (RSV and PT) plus Q account for 6 people (R, S, V, P, T, Q). The remaining person is U.

Step 3: Placing the RSV Block

The RSV block requires 3 consecutive days. Let's see where it can fit:

• It cannot include Wednesday because Q is scheduled on Wednesday.
• Possible slots for RSV: (Mon, Tue, Wed) - No (Q=Wed); (Tue, Wed, Thu) - No (Q=Wed); (Wed, Thu, Fri) - No (Q=Wed); (Thu, Fri, Sat); (Fri, Sat, Sun).

So, the RSV block must be either from Thursday to Saturday OR from Friday to Sunday.

Step 4: Analyzing the T and U Constraint

Exactly 4 people have exams between T and U. Since there are 7 people in total, this means T and U must be positioned such that there are 4 people separating them. The possible day positions for T and U are (Monday, Saturday) or (Tuesday, Sunday), considering the order does not matter yet. The clue also states neither T nor U has an exam on Monday.

• This eliminates the (Monday, Saturday) possibility for T and U.
• Therefore, T and U must be on Tuesday and Sunday (in some order).

Step 5: Combining Constraints and Testing Scenarios

We know Q is on Wednesday, and T/U are on Tuesday and Sunday.

Scenario 1: T is on Tuesday, U is on Sunday.

• The schedule looks like: _, T, Q, _, _, _, U
• We need to place the PT block. Since T is on Tuesday, P must be on Monday.
• Current schedule: P, T, Q, _, _, _, U
• The remaining days are Thursday, Friday, Saturday. The remaining people are R, S, V. They must fit the RSV block.
• Place RSV in the remaining slots: Thursday(R), Friday(S), Saturday(V).
• Final Schedule (Scenario 1):

• Let's verify all clues:
  • Q on Wed: Yes.
  • 4 people between T (Tue) and U (Sun): Q, R, S, V. Yes.
  • Neither T nor U on Mon: Yes (T=Tue, U=Sun).
  • R immediately before S: Yes (R=Thu, S=Fri).
  • V immediately after S: Yes (S=Fri, V=Sat).
  • P immediately before T: Yes (P=Mon, T=Tue).
• Calculate the answer: How many people between P (Monday) and R (Thursday)? The people are T (Tuesday) and Q (Wednesday). There are 2 people.

Scenario 2: U is on Tuesday, T is on Sunday.

• The schedule looks like: _, U, Q, _, _, _, T
• We need to place the PT block. Since T is on Sunday, P must be on Saturday.
• Current schedule: _, U, Q, _, _, P, T
• We need to place the RSV block (3 consecutive days) in the remaining slots: Monday, Thursday, Friday.
• Can RSV fit? The available slots are Mon, Thu, Fri. These are not consecutive. The only consecutive slots left are (Thu, Fri, Sat), but P is on Saturday. Therefore, this scenario is impossible.

Step 6: Conclusion

The only valid schedule derived from the clues is:

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

Based on this schedule, the people with exams between P (on Monday) and R (on Thursday) are T and Q. Therefore, there are 2 people between P and R.