Question 1
Five subjects are scheduled on five different days of the week (Monday to Friday), one subject per day. The following information is given:
- English is scheduled on Wednesday
- History is scheduled immediately after Physics
- There are exactly two classes between Chemistry and Mathematics
- Physics is not on Monday
On which day is History scheduled?
Step-by-step solution:
Table Method:
1. Create a timeline for Monday to Friday
2. Apply direct constraints:
- English is on Wednesday (fixed)
- Physics is not on Monday
3. Apply consecutive constraint:
- History immediately follows Physics
- Possible pairs: (Tue-Wed), (Wed-Thu), (Thu-Fri)
- Since Wednesday is occupied, options are (Tue-Wed) or (Thu-Fri)
4. Apply gap constraint:
- Two classes between Chemistry and Mathematics
5. Final schedule:
- Monday: Chemistry
- Tuesday: Physics
- Wednesday: English
- Thursday: History
- Friday: Mathematics
Answer: History is scheduled on Thursday
Key Strategy: Fix direct constraints first, then work with consecutive and gap constraints.
Table Method:
1. Create a timeline for Monday to Friday
2. Apply direct constraints:
- English is on Wednesday (fixed)
- Physics is not on Monday
3. Apply consecutive constraint:
- History immediately follows Physics
- Possible pairs: (Tue-Wed), (Wed-Thu), (Thu-Fri)
- Since Wednesday is occupied, options are (Tue-Wed) or (Thu-Fri)
4. Apply gap constraint:
- Two classes between Chemistry and Mathematics
5. Final schedule:
- Monday: Chemistry
- Tuesday: Physics
- Wednesday: English
- Thursday: History
- Friday: Mathematics
Answer: History is scheduled on Thursday
Key Strategy: Fix direct constraints first, then work with consecutive and gap constraints.