Exam Scheduling Logic Puzzle Solution
This problem requires determining the order of exams for seven people (K, L, U, G, A, B, W) throughout a week (Monday to Sunday) based on several given conditions.
Step 1: Establish the Weekly Schedule Framework
We represent the week as follows:
- Monday
- Tuesday
- Wednesday
- Thursday
- Friday
- Saturday
- Sunday
Step 2: Place Known Exam Dates
From the problem statement:
- K has an exam on Tuesday.
- U has an exam on Sunday.
Current Schedule:
- Monday:
- Tuesday: K
- Wednesday:
- Thursday:
- Friday:
- Saturday:
- Sunday: U
Step 3: Apply Sequential Constraints
Analyze the conditions related to adjacent days:
- "G has exam on the day immediately before U." Since U is on Sunday, G must be on Saturday.
- "L has exam on the day immediately before G." Since G is on Saturday, L must be on Friday.
- "W has exam on the day immediately after K." Since K is on Tuesday, W must be on Wednesday.
Updated Schedule:
- Monday:
- Tuesday: K
- Wednesday: W
- Thursday:
- Friday: L
- Saturday: G
- Sunday: U
Step 4: Apply the "Between" Constraint
Consider the condition: "Only three people have exams between B and L."
- L's exam is on Friday.
- We need to find a position for B such that there are exactly 3 days (people) between B's exam day and L's exam day (Friday).
- If B is placed on Monday, the days between Monday and Friday are Tuesday, Wednesday, and Thursday. This satisfies the condition of 3 people between B and L.
- Let's verify this placement: Monday (B), Tuesday (K), Wednesday (W), Thursday (?), Friday (L). The people between B and L are K, W, and the person on Thursday. This fits perfectly.
- Therefore, B has an exam on Monday.
Updated Schedule:
- Monday: B
- Tuesday: K
- Wednesday: W
- Thursday:
- Friday: L
- Saturday: G
- Sunday: U
Step 5: Determine the Final Exam Slot
- The only remaining person is A.
- The only remaining day is Thursday.
- Therefore, A has an exam on Thursday.
Step 6: Final Schedule and Answer Calculation
The complete exam schedule is:
| Day | Person |
|---|---|
| Monday | B |
| Tuesday | K |
| Wednesday | W |
| Thursday | A |
| Friday | L |
| Saturday | G |
| Sunday | U |
The question asks: "How many people have exams before A?"
- A's exam is on Thursday.
- The days before Thursday are Monday, Tuesday, and Wednesday.
- The people with exams on these days are B, K, and W.
- Therefore, 3 people have exams before A.
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?
