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 Math.
- Sahil did not take 72 minutes and is not ranked 4.
- The fastest finisher attempted Chemistry.
- The one ranked 3 took more time than Nihal.
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
--- | --- | --- | ---
Hina | 1 | 30 | Art
Vihaan | 2 | 34 | Math
Sahil | 3 | 72 | Music
Yash | 4 | 35 | Chemistry
Nihal | 5 | 40 | Science
Integrate constraints across dimensions and validate uniqueness.
Verification:
- The student ranked 1 finished earlier than the one who attempted Math.
- Sahil did not take 72 minutes and is not ranked 4.
- The fastest finisher attempted Chemistry.
- The one ranked 3 took more time than Nihal.
Set up a table: Student x (Rank, Time, Subject). Use rank-time inequalities and subject anchors (fastest subject).
Student | Rank | Time(min) | Subject
--- | --- | --- | ---
Hina | 1 | 30 | Art
Vihaan | 2 | 34 | Math
Sahil | 3 | 72 | Music
Yash | 4 | 35 | Chemistry
Nihal | 5 | 40 | Science
Integrate constraints across dimensions and validate uniqueness.
Verification:
- The student ranked 1 finished earlier than the one who attempted Math.
- Sahil did not take 72 minutes and is not ranked 4.
- The fastest finisher attempted Chemistry.
- The one ranked 3 took more time than Nihal.