Who has an exam on Monday?
Solving the Weekly Exam Schedule Logic Puzzle
This puzzle involves scheduling exams for seven individuals (P, Q, R, S, T, U, V) on distinct days of a week, from Monday to Sunday. We must deduce the schedule based on the given conditions to find who has an exam on Monday.
Step 1: Setting up the Schedule Framework
We represent the days of the week:
- Monday
- Tuesday
- Wednesday
- Thursday
- Friday
- Saturday
- Sunday
Step 2: Placing the Known Exam Day
The problem states that R has an exam on Friday.
Initial Schedule:
| Mon | Tue | Wed | Thu | Fri | Sat | Sun |
| _ | _ | _ | _ | R | _ | _ |
Step 3: Determining Q's Exam Day
There are exactly 2 people with exams scheduled between R and Q.
- Given R is on Friday, the only way to have exactly two people between R and Q is if Q's exam is on Tuesday (Q, Wednesday, Thursday, R).
Updated Schedule:
| Mon | Tue | Wed | Thu | Fri | Sat | Sun |
| _ | Q | _ | _ | R | _ | _ |
Step 4: Identifying Consecutive Exam Blocks
Two pairs have exams on consecutive days:
- S is immediately before U (forming an 'SU' block).
- V is immediately before P (forming a 'VP' block).
The days available for these blocks are Monday, Wednesday, Thursday, Saturday, and Sunday.
The only available two-day slots are (Wednesday, Thursday) and (Saturday, Sunday).
Step 5: Using the T and U Constraint to Finalize the Schedule
There are exactly 2 people with exams between T and U.
We test the two possible arrangements for the SU and VP blocks:
- Arrangement 1: SU block on (Wednesday, Thursday) and VP block on (Saturday, Sunday).
- The schedule becomes: Mon(_), Tue(Q), Wed(S), Thu(U), Fri(R), Sat(V), Sun(P).
- The remaining person, T, must take the remaining day, Monday.
- Full Schedule: Mon(T), Tue(Q), Wed(S), Thu(U), Fri(R), Sat(V), Sun(P).
- Check constraint: T (Mon) and U (Thu). The people between them are Q (Tue) and S (Wed). This fits the condition of 2 people. This arrangement is valid.
- Arrangement 2: SU block on (Saturday, Sunday) and VP block on (Wednesday, Thursday).
- The schedule becomes: Mon(_), Tue(Q), Wed(V), Thu(P), Fri(R), Sat(S), Sun(U).
- The remaining person, T, must take the remaining day, Monday.
- Full Schedule: Mon(T), Tue(Q), Wed(V), Thu(P), Fri(R), Sat(S), Sun(U).
- Check constraint: T (Mon) and U (Sun). The people between them are Q, V, P, R, S (Tue, Wed, Thu, Fri, Sat). This is 5 people, which violates the condition of 2 people. This arrangement is invalid.
Final Conclusion
Only Arrangement 1 satisfies all given conditions. The confirmed weekly schedule is:
| Day | Person |
| Monday | T |
| Tuesday | Q |
| Wednesday | S |
| Thursday | U |
| Friday | R |
| Saturday | V |
| Sunday | P |
Therefore, T has an exam on Monday.
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