Exam Schedule Logic Puzzle Explained

This problem involves determining the exam schedule for seven people (M, N, O, P, Q, R, S) across a week (Monday to Sunday), based on a set of given conditions. We need to find the specific day on which Q has their exam.

Understanding the Constraints

• Seven individuals: M, N, O, P, Q, R, S.
• Seven days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.
• Each person has an exam on a unique day.
• Condition 1: S's exam is on Friday.
• Condition 2: Exactly two people have exams between S and R.
• Condition 3: O's exam is immediately before N's exam (O -> N).
• Condition 4: M's exam is immediately after P's exam (P -> M).
• Condition 5: S's exam day is after M's exam day (M < S).

Step-by-Step Deduction

Let's break down the problem step-by-step:

We know S has an exam on Friday. Let's represent the week:

Condition 2 states that exactly two people have exams between S (Friday) and R.

• If R were scheduled after S: The days available after Friday are Saturday and Sunday. It's impossible to fit two people *between* S and R in this scenario.
• Therefore, R must be scheduled before S. The sequence must look like R _ _ S. This implies there are exactly 3 days separating R and S.
• Since S is on Friday, we count back 3 days to find R's day: Thursday (1 day between), Wednesday (2 days between), Tuesday (3 days between). This places R on Tuesday.

Updated schedule:

The days between R (Tuesday) and S (Friday) are Wednesday and Thursday. This confirms that two people are scheduled between R and S.

Condition 5 states S (Friday) is scheduled after M. This means M must be scheduled on a day before Friday. Possible days for M are Monday, Tuesday, Wednesday, or Thursday.

However, we know R is scheduled on Tuesday, so M cannot be on Tuesday.

Condition 4 states M's exam is immediately after P's exam (P -> M).

• If M were scheduled on Monday, P couldn't be placed immediately before M. This is impossible.
• If M were scheduled on Wednesday, P would have to be on Tuesday. But R is scheduled on Tuesday, so this is impossible.
• The only remaining possibility is that M is scheduled on Thursday. This means P must be scheduled on Wednesday.

Updated schedule:

Condition 3 states O has an exam immediately before N (O -> N).

Looking at the current schedule, the days filled are Tuesday, Wednesday, Thursday, and Friday. The remaining days are Monday, Saturday, and Sunday. The only consecutive available slots are Saturday and Sunday.

Therefore, O must be scheduled on Saturday, and N must be scheduled on Sunday.

Updated schedule:

The only person left to schedule is Q, and the only day remaining is Monday.

Therefore, Q must have their exam on Monday.

Let's verify the complete schedule against all given conditions:

• Final Schedule: Q(Mon), R(Tue), P(Wed), M(Thu), S(Fri), O(Sat), N(Sun)
• S on Friday? Yes.
• Two people between S and R? R is on Tuesday, S is on Friday. The people scheduled on Wednesday (P) and Thursday (M) are between them. Yes, condition met.
• O immediately before N? O is on Saturday, N is on Sunday. Yes, condition met.
• M immediately after P? P is on Wednesday, M is on Thursday. Yes, condition met.
• S after M? M is on Thursday, S is on Friday. Yes, condition met.

All conditions are satisfied with this arrangement.

Final Exam Schedule

Based on this deduction, Q has an exam on Monday.