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