Question 1
A conference needs to schedule 6 sessions across 3 time slots and 3 rooms. Each room can hold one session per slot. The constraints are:
- Prof. Brown can only speak at 11:00-12:00
- Data Science and Blockchain cannot be in the same time slot
- Prof. Jones and Prof. Wilson must speak in consecutive time slots
- Robotics must be in Hall A
Which speaker presents the Blockchain session?
Step-by-step solution:
Scheduling Grid Analysis:
1. Fix direct constraints:
- Prof. Brown at 11:00-12:00
- Robotics in Hall A
2. Apply consecutive constraint: Prof. Jones and Prof. Wilson in consecutive slots
3. Apply conflict constraint: Data Science and Blockchain not together
4. Final Schedule:
9:00-10:00:
- Hall A: Robotics by Prof. Jones
- Hall B: Cybersecurity by Dr. Taylor
- Hall C: Blockchain by Dr. Lee
10:00-11:00:
- Hall A: Machine Learning by Prof. Wilson
- Hall B: Cloud Computing by Dr. Chen
- Hall C: (empty)
11:00-12:00:
- Hall A: Data Science by Prof. Brown
- Hall B: (empty)
- Hall C: (empty)
Answer: Dr. Lee presents Blockchain
Key Strategy: Use a grid to solve the assignment problem and satisfy all constraints sequentially.
Scheduling Grid Analysis:
1. Fix direct constraints:
- Prof. Brown at 11:00-12:00
- Robotics in Hall A
2. Apply consecutive constraint: Prof. Jones and Prof. Wilson in consecutive slots
3. Apply conflict constraint: Data Science and Blockchain not together
4. Final Schedule:
9:00-10:00:
- Hall A: Robotics by Prof. Jones
- Hall B: Cybersecurity by Dr. Taylor
- Hall C: Blockchain by Dr. Lee
10:00-11:00:
- Hall A: Machine Learning by Prof. Wilson
- Hall B: Cloud Computing by Dr. Chen
- Hall C: (empty)
11:00-12:00:
- Hall A: Data Science by Prof. Brown
- Hall B: (empty)
- Hall C: (empty)
Answer: Dr. Lee presents Blockchain
Key Strategy: Use a grid to solve the assignment problem and satisfy all constraints sequentially.