Understanding the Exam Schedule Constraints

The problem asks us to determine the number of people with exams scheduled after person Q, based on a set of rules about exam dates during a single week (Monday to Sunday).

We have 7 individuals: P, Q, R, S, T, U, and V.

Here are the key constraints:

• Each person has an exam on a different day of the week.
• V's Exam Day: V's exam is on Thursday.
• U and Q Exam Spacing: Exactly 4 people have exams between U and Q. This implies a 5-day gap between U's and Q's exam days (e.g., Monday and Saturday).
• U and Q Sunday Exclusion: Neither U nor Q has an exam on Sunday.
• T and S Consecutive Exams: T's exam is immediately before S's exam. They form a block: TS.
• R's Friday Exclusion: R does not have an exam on Friday.
• U and S Order: U's exam day must be before S's exam day (U is not scheduled after S).

Mapping Exams to Days

Let's represent the week's days:

Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday

We know V is on Thursday:

The constraint "4 people between U and Q" means U and Q must be 5 days apart. Considering V is on Thursday, the only possible pairs of days are Monday and Saturday.

Exploring Possible Scenarios for U and Q

Scenario 1: U on Monday, Q on Saturday

This arrangement fits the 5-day gap:

This satisfies:

• 4 people (on Tue, Wed, Thu, Fri) are between U and Q.
• U (Mon) and Q (Sat) are not on Sunday.
• V is on Thursday.

Remaining days: Tuesday, Wednesday, Friday, Sunday.

Remaining people: P, R, S, T.

We need to place the 'TS' block (T immediately before S).

Possible slots for TS:

• Tuesday-Wednesday: This works.
• Wednesday-Thursday: Impossible, V is on Thursday.
• Thursday-Friday: Impossible, V is on Thursday.
• Friday-Saturday: Impossible, Q is on Saturday.
• Saturday-Sunday: Impossible, Q is on Saturday.
• Sunday-Monday: Impossible, U is on Monday.

Therefore, T must be on Tuesday and S on Wednesday.

Now, check the constraint "U does not have an exam after S". U is on Monday, and S is on Wednesday. Since Monday comes before Wednesday, this condition is satisfied.

The remaining people are P and R. The remaining days are Friday and Sunday.

R cannot have an exam on Friday. So, R must take the Sunday slot, and P must take the Friday slot.

The final schedule is:

This schedule satisfies all given conditions.

Scenario 2: Q on Monday, U on Saturday

This arrangement also fits the 5-day gap:

This satisfies:

• 4 people (on Tue, Wed, Thu, Fri) are between Q and U.
• Q (Mon) and U (Sat) are not on Sunday.
• V is on Thursday.

Remaining days: Tuesday, Wednesday, Friday, Sunday.

Remaining people: P, R, S, T.

Place the 'TS' block. The only possible slot is Tuesday-Wednesday.

Now, check the constraint "U does not have an exam after S". Here, U is on Saturday, and S is on Wednesday. Since Saturday comes *after* Wednesday, this scenario violates the constraint.

Therefore, Scenario 2 is not possible.

Final Calculation: People Examined After Q

The only valid schedule is:

Monday: U

Tuesday: T

Wednesday: S

Thursday: V

Friday: P

Saturday: Q

Sunday: R

Q's exam is on Saturday.

We need to count how many people have exams *after* Saturday.

The only day after Saturday is Sunday.

R has an exam on Sunday.

Thus, there is exactly 1 person (R) who has an exam after Q.