Question 1
A conference needs to schedule 5 sessions across 3 time slots and 3 rooms. Each room can hold one session per slot. The constraints are:
- Dr. Taylor can only speak at 10:00-11:00
- Data Science and IoT cannot be in the same time slot
- Dr. Chen and Prof. Brown must speak in consecutive time slots
- IoT must be in Hall A
Which speaker presents the IoT session?
Step-by-step solution:
Scheduling Grid Analysis:
1. Fix direct constraints:
- Dr. Taylor at 10:00-11:00
- IoT in Hall A
2. Apply consecutive constraint: Dr. Chen and Prof. Brown in consecutive slots
3. Apply conflict constraint: Data Science and IoT not together
4. Final Schedule:
9:00-10:00:
- Hall A: IoT by Prof. Jones
- Hall B: Robotics by Dr. Chen
- Hall C: Data Science by Dr. Smith
10:00-11:00:
- Hall A: AI Ethics by Dr. Taylor
- Hall B: Blockchain by Prof. Brown
- Hall C: (empty)
11:00-12:00:
- Hall A: (empty)
- Hall B: (empty)
- Hall C: (empty)
Answer: Prof. Jones presents IoT
Key Strategy: Use a grid to solve the assignment problem and satisfy all constraints sequentially.
Scheduling Grid Analysis:
1. Fix direct constraints:
- Dr. Taylor at 10:00-11:00
- IoT in Hall A
2. Apply consecutive constraint: Dr. Chen and Prof. Brown in consecutive slots
3. Apply conflict constraint: Data Science and IoT not together
4. Final Schedule:
9:00-10:00:
- Hall A: IoT by Prof. Jones
- Hall B: Robotics by Dr. Chen
- Hall C: Data Science by Dr. Smith
10:00-11:00:
- Hall A: AI Ethics by Dr. Taylor
- Hall B: Blockchain by Prof. Brown
- Hall C: (empty)
11:00-12:00:
- Hall A: (empty)
- Hall B: (empty)
- Hall C: (empty)
Answer: Prof. Jones presents IoT
Key Strategy: Use a grid to solve the assignment problem and satisfy all constraints sequentially.