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?
Three
This problem involves determining the order of exams for seven people (J, K, L, M, N, O, P) across a week (Monday to Sunday) based on several given conditions.
Step-by-Step Deduction of the Exam Schedule
We are given the following clues:
- The week starts on Monday and ends on Sunday.
- Clue 1: Only two people have exams before P. This means P's exam is on the 3rd day of the week. Since the week starts on Monday, P has an exam on Wednesday.
- Order: Mon, Tue, P (Wed), Thu, Fri, Sat, Sun
- Clue 2: Only one person has an exam after L. This means L's exam is on the 6th day of the week, which is Saturday.
- Order: Mon, Tue, P (Wed), Thu, Fri, L (Sat), Sun
- Clue 3: Only three people have exams between P and J. We know P is on Wednesday. If there are three people between P and J, and L is on Saturday, J must be on Sunday.
- P (Wed), Person1, Person2, Person3, J (Sun). The days between Wed and Sun are Thu, Fri, Sat. This fits the condition.
- Order: Mon, Tue, P (Wed), Thu, Fri, Sat, J (Sun)
- Clue 4: Only one person has an exam between K and L. L is on Saturday. To have one person between them, K must be on Thursday.
- K (Thu), Person1, L (Sat). The person between them is Friday. This fits the condition.
- Order: Mon, Tue, P (Wed), K (Thu), Fri, L (Sat), J (Sun)
- Clue 5: O has an exam immediately after M. This means M and O form a block (M, O).
Determining the Positions of M, O, and N
From the deduced schedule, we have:
- Wednesday: P
- Thursday: K
- Saturday: L
- Sunday: J
The remaining days are Monday, Tuesday, and Friday. The remaining people are M, N, and O.
Since M and O must have their exams consecutively (M immediately followed by O), they must occupy Monday and Tuesday.
- Monday: M
- Tuesday: O
This leaves Friday for the last person, N.
- Friday: N
Final Exam Schedule
The complete schedule is:
| Day | Person |
| Monday | M |
| Tuesday | O |
| Wednesday | P |
| Thursday | K |
| Friday | N |
| Saturday | L |
| Sunday | J |
Calculating Exams Between M and N
We need to find the number of people who have exams between M and N.
- M's exam is on Monday.
- N's exam is on Friday.
The people with exams between Monday and Friday are:
- Tuesday: O
- Wednesday: P
- Thursday: K
Therefore, there are 3 people who have exams between M and N.
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 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?
