A has an exam on Saturday. Only 4 people have exams between M and O, neither of whom has an exam on Monday. I has an exam immediately after Q, and W has an exam immediately before Q. O has an exam after I.
How many people have exams after I?
Exam Schedule Analysis
The problem requires determining the exam schedule for 7 people (A, C, I, M, O, Q, W) across 7 days (Monday to Sunday) based on several conditions.
Constraint Breakdown
- Days: Monday (1) to Sunday (7).
- Fixed Position: A has an exam on Saturday (Day 6).
- Consecutive Block: W, Q, and I have exams consecutively in that order (WQI block).
- Relative Position: O has an exam after I.
- Separation Constraint: Exactly 4 people have exams between M and O. This means M and O are 5 days apart (e.g., Day 2 and Day 7).
- Exclusion Constraint: M and O do not have exams on Monday (Day 1).
Deductive Steps
- M & O Placement: Since M and O cannot be on Monday and must be 5 days apart, the only possible pairs of days are (Tuesday, Sunday) or (Sunday, Tuesday).
- WQI Block Placement: The WQI block needs 3 consecutive days. O must be after I. A is on Day 6.
- Testing Possibilities:
- If M=Tue (2) and O=Sun (7): Days left for WQI are Mon, Wed, Thu, Fri. This doesn't allow 3 consecutive days.
- If O=Tue (2) and M=Sun (7): Days left for WQI are Mon, Wed, Thu, Fri. This also doesn't allow 3 consecutive days.
- Consider other placements for WQI. If WQI are Wed(3), Thu(4), Fri(5). This leaves Mon(1), Tue(2), Sun(7) for C, M, O.
- If W=Wed(3), Q=Thu(4), I=Fri(5): O must be after I, so O must be Sun(7). M cannot be Mon(1), so M must be Tue(2). This fits the 5-day gap (Tue to Sun).
- Final Schedule Derivation: Based on the successful placement:
- W = Wednesday (3)
- Q = Thursday (4)
- I = Friday (5)
- O = Sunday (7) (after I)
- A = Saturday (6)
- M = Tuesday (2) (fits the 4 people between M and O: Wed, Thu, Fri, Sat)
- C = Monday (1) (the remaining person and day)
Answer Calculation
The question asks how many people have exams after I.
- I has an exam on Friday (Day 5).
- The days after Friday are Saturday (Day 6) and Sunday (Day 7).
- The people scheduled on these days are A (Saturday) and O (Sunday).
- Therefore, 2 people have exams after I.
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?
