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. Jones can only speak at 9:00-10:00
- Blockchain and Cloud Computing cannot be in the same time slot
- Dr. Chen and Prof. Jones must speak in consecutive time slots
- Data Science must be in Hall B
Which speaker presents the Blockchain session?
Step-by-step solution:
Scheduling Grid Analysis:
1. Fix direct constraints:
- Prof. Jones at 9:00-10:00
- Data Science in Hall B
2. Apply consecutive constraint: Dr. Chen and Prof. Jones in consecutive slots
3. Apply conflict constraint: Blockchain and Cloud Computing not together
4. Final Schedule:
9:00-10:00:
- Hall A: Cloud Computing by Dr. Taylor
- Hall B: Robotics by Prof. Jones
- Hall C: Blockchain by Prof. Garcia
10:00-11:00:
- Hall A: IoT by Dr. Smith
- Hall B: Data Science by Prof. Brown
- Hall C: Cybersecurity by Dr. Chen
11:00-12:00:
- Hall A: (empty)
- Hall B: (empty)
- Hall C: (empty)
Answer: Prof. Garcia 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. Jones at 9:00-10:00
- Data Science in Hall B
2. Apply consecutive constraint: Dr. Chen and Prof. Jones in consecutive slots
3. Apply conflict constraint: Blockchain and Cloud Computing not together
4. Final Schedule:
9:00-10:00:
- Hall A: Cloud Computing by Dr. Taylor
- Hall B: Robotics by Prof. Jones
- Hall C: Blockchain by Prof. Garcia
10:00-11:00:
- Hall A: IoT by Dr. Smith
- Hall B: Data Science by Prof. Brown
- Hall C: Cybersecurity by Dr. Chen
11:00-12:00:
- Hall A: (empty)
- Hall B: (empty)
- Hall C: (empty)
Answer: Prof. Garcia presents Blockchain
Key Strategy: Use a grid to solve the assignment problem and satisfy all constraints sequentially.