Determining the Exam Schedule
We need to determine the exact day of the week for each person's exam (C, D, E, F, S, T, U) from Monday to Sunday, based on the given clues.
Clue 1: F's Exam Day
F has the exam on Friday. Let's represent the week:
- Monday:
- Tuesday:
- Wednesday:
- Thursday:
- Friday: F
- Saturday:
- Sunday:
Clue 2: T and F's Exam Relation
Only two people have their exams between T and F. Since F is on Friday, T cannot be on Monday (3 people between) or Saturday/Sunday (less than 2 people between). If T is on Tuesday, the days between are Wednesday and Thursday (2 people). This fits the condition.
- Monday:
- Tuesday: T
- Wednesday:
- Thursday:
- Friday: F
- Saturday:
- Sunday:
Clue 3: E and T's Exam Relation
Only four people have their exams between E and T. T is on Tuesday. If E is on Sunday, the days between are Wednesday, Thursday, Friday, and Saturday (4 people). This fits the condition.
- Monday:
- Tuesday: T
- Wednesday:
- Thursday:
- Friday: F
- Saturday:
- Sunday: E
Clue 4: U and S's Exam Relation
S has the exam immediately after U. The remaining days are Monday, Wednesday, Thursday, and Saturday. The only consecutive days available for U and S are Wednesday and Thursday.
- Monday:
- Tuesday: T
- Wednesday: U
- Thursday: S
- Friday: F
- Saturday:
- Sunday: E
Clue 5: D's Exam Day Restriction
The remaining people are C and D. The remaining days are Monday and Saturday. D does not have the exam on Monday. Therefore, D must have the exam on Saturday, and C must have the exam on Monday.
- Monday: C
- Tuesday: T
- Wednesday: U
- Thursday: S
- Friday: F
- Saturday: D
- Sunday: E
This completes the schedule.
Answering the Final Question
The question asks: How many people have their exams before D and after C?
Identify the people before D (Saturday): C, T, U, S, F. (Total 5 people)
Identify the people after C (Monday): T, U, S, F, D, E. (Total 6 people)
We need the people who satisfy BOTH conditions (after C AND before D).
These people are T, U, S, and F.
Calculating the Count:
The set of people after C is {T, U, S, F, D, E}.
The set of people before D is {C, T, U, S, F}.
The intersection of these two sets is {T, U, S, F}.
The number of people in the intersection is 4.
Therefore, four people have their exams before D and after C.
Important Questions from Scheduling Puzzle
- Each of O, P, Q, R, S, T and U has an exam on a different day of a week starting from Monday and ending on Sunday of the same week. S has an exam on Wednesday. R has an exam on one of the days after P and T has an exam on one of the days before Q. U has an exam immediately after O and S has an exam immediately before O. T has an exam on one of the days after U. How many people have an exam between S and Q?
- Each of M, N, O, P, Q, R and S has an exam on a different day of the week, starting from Monday and ending on Sunday of the same week. S has an exam on Friday. Only two people have exams between S and R. O has an exam immediately before N. M has an exam immediately after P. S has an exam on one of the days after M. On which day does Q have an exam?
- Each of C, D, E, F, S, T and U has an exam on a different day of a week starting from Monday and ending on Sunday of the same week. S has the exam on Thursday and T has the exam on Saturday. F has the exam immediately before U. C has the exam on one of the days after E. D has the exam immediately after U. Who has the exam on the last day of the week?
Each of J, K, L, M, N, O and P has an exam on a different day of a week starting from Monday and ending on Sunday of the same week. Only two people have exams before P. Only one person has an exam after L. Only three people have exams between P and J. Only one person has an exam between K and L. O has an exam immediately after M.
How many people have exams between M and N?Each of C, D, E, F, S, T and U has an exam on a different day of a week starting from Monday and ending on Sunday of the same week. No one has an exam before D. Only three people have their exams between D and T. Only one person has the exam between T and S. C has the exam on Wednesday. E has the exam on one of the days after F but on one of the days before U. On which day of the week does E have the exam?
