S has an exam on Friday. Only two people have exams between G and S. Only four people have exams between M and G. J has an exam immediately after T. R does not have an exam on Monday.
How many people have exams between R and O?
This problem requires deducing the exam schedule for seven people (G, J, M, O, R, S, T) over seven days (Monday to Sunday) using given clues.
Determining Exam Schedule
Let's map the days: Mon, Tue, Wed, Thu, Fri, Sat, Sun.
- Clue 1: S has an exam on Friday.
Mon Tue Wed Thu S Sat Sun
- Clue 2: Only two people have exams between G and S.
- If G is before S: G _ _ S. This means G is 3 days before Friday, which is Tuesday.
Mon G Wed Thu S Sat Sun
- If G is after S: S _ _ G. This means G is 3 days after Friday, which is Monday. (Let's verify later).
G Tue Wed Thu S Sat Sun
- If G is before S: G _ _ S. This means G is 3 days before Friday, which is Tuesday.
- Clue 3: Only four people have exams between M and G.
- Using G on Tuesday: M _ _ _ _ G. M would be 5 days before Tuesday, which is impossible (only Monday is before Tuesday). So M must be after G. G _ _ _ _ M. M would be 5 days after Tuesday, which is Sunday.
Mon G Wed Thu Fri Sat M
This arrangement works: G (Tue) and M (Sun) have 4 days (Wed, Thu, Fri, Sat) between them. - Let's re-check G on Monday: M _ _ _ _ G (Monday). M would be 5 days before Monday, impossible. G _ _ _ _ M (Monday). M would be 5 days after Monday, which is Saturday.
G Tue Wed Thu Fri M Sun
In this case, G (Mon) and M (Sat) have 4 days (Tue, Wed, Thu, Fri) between them. This also seems valid initially.
- Using G on Tuesday: M _ _ _ _ G. M would be 5 days before Tuesday, which is impossible (only Monday is before Tuesday). So M must be after G. G _ _ _ _ M. M would be 5 days after Tuesday, which is Sunday.
- Clue 4: J has an exam immediately after T (TJ sequence).
- Scenario 1 (G=Tue, M=Sun): Remaining days are Mon, Wed, Thu, Sat. The only consecutive pair is Wed, Thu. So T=Wed, J=Thu.
Mon G T J Fri Sat M
- Scenario 2 (G=Mon, M=Sat): Remaining days are Tue, Wed, Thu, Sun. No consecutive pair for TJ. This scenario is invalid.
- Scenario 1 (G=Tue, M=Sun): Remaining days are Mon, Wed, Thu, Sat. The only consecutive pair is Wed, Thu. So T=Wed, J=Thu.
- Clue 5: R does not have an exam on Monday. The remaining people are R and O. The remaining days are Monday and Saturday. Since R cannot be on Monday, R must be on Saturday. This leaves O for Monday.
Final Exam Schedule
The deduced schedule is:
Monday: O
Tuesday: G
Wednesday: T
Thursday: J
Friday: S
Saturday: R
Sunday: M
Calculating Exams Between R and O
We need to find the number of people with exams between R (Saturday) and O (Monday).
- O has an exam on Monday.
- R has an exam on Saturday.
- The days between Monday and Saturday are Tuesday, Wednesday, Thursday, and Friday.
- The people with exams on these days are G, T, J, and S.
- Therefore, there are 4 people with exams between R and O.
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 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. F has the exam on Friday. Only two people have their exams between T and F. Only four people have their exams between E and T. S has the exam immediately after U. D does not have the exam on Monday. How many people have their exams before D and after C?
- 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?
