Question 1
Five students attempted a test and received distinct ranks (1 best to 5 worst), took distinct times, and attempted distinct subjects. Use the clues:
- The student ranked 1 finished earlier than the one who attempted English.
- Laksh did not take 62 minutes and is not ranked 4.
- The fastest finisher attempted History.
- The one ranked 3 took more time than Xavier.
Question: Who secured Rank 1?
Multi-Parameter Optimization
Set up a table: Student x (Rank, Time, Subject). Use rank-time inequalities and subject anchors (fastest subject).
Student | Rank | Time(min) | Subject
--- | --- | --- | ---
Sahil | 1 | 45 | Science
Jatin | 2 | 51 | English
Laksh | 3 | 62 | Physics
Gaurav | 4 | 39 | History
Xavier | 5 | 68 | Chemistry
Integrate constraints across dimensions and validate uniqueness.
Verification:
- The student ranked 1 finished earlier than the one who attempted English.
- Laksh did not take 62 minutes and is not ranked 4.
- The fastest finisher attempted History.
- The one ranked 3 took more time than Xavier.
Set up a table: Student x (Rank, Time, Subject). Use rank-time inequalities and subject anchors (fastest subject).
Student | Rank | Time(min) | Subject
--- | --- | --- | ---
Sahil | 1 | 45 | Science
Jatin | 2 | 51 | English
Laksh | 3 | 62 | Physics
Gaurav | 4 | 39 | History
Xavier | 5 | 68 | Chemistry
Integrate constraints across dimensions and validate uniqueness.
Verification:
- The student ranked 1 finished earlier than the one who attempted English.
- Laksh did not take 62 minutes and is not ranked 4.
- The fastest finisher attempted History.
- The one ranked 3 took more time than Xavier.