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:
- Physics is scheduled on Wednesday
- English is scheduled immediately after Mathematics
- There are exactly two classes between Biology and History
- Mathematics is not on Monday
On which day is English scheduled?
Step-by-step solution:
Table Method:
1. Create a timeline for Monday to Friday
2. Apply direct constraints:
- Physics is on Wednesday (fixed)
- Mathematics is not on Monday
3. Apply consecutive constraint:
- English immediately follows Mathematics
- 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 Biology and History
5. Final schedule:
- Monday: Biology
- Tuesday: History
- Wednesday: Physics
- Thursday: Mathematics
- Friday: English
Answer: English is scheduled on Friday
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:
- Physics is on Wednesday (fixed)
- Mathematics is not on Monday
3. Apply consecutive constraint:
- English immediately follows Mathematics
- 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 Biology and History
5. Final schedule:
- Monday: Biology
- Tuesday: History
- Wednesday: Physics
- Thursday: Mathematics
- Friday: English
Answer: English is scheduled on Friday
Key Strategy: Fix direct constraints first, then work with consecutive and gap constraints.