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Scheduling - Intermediate-Advanced Level: timetable puzzles INTERMEDIATE-ADVANCED

Strategic expert challenge ★ for scheduling: 20 intermediate-advanced-level problems. Worksheet 19 of 30 - Focus: timetable puzzles. Develop expertise in appointment logic, calendar scheduling, shift planning with step-by-step solutions. Ideal for advanced developing learners targeting advanced concepts with increasing complexity.

📝 Worksheet 19 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate-advanced level

What you'll learn in this worksheet:
Your progress through Scheduling
Worksheet 19 of 30 (63% complete)

Question 1

Four team members (David, Eva, Alice, Bob) must be assigned to four unique tasks (Documentation, Deployment, Design, Testing). The assignments must follow these rules: 1. David must handle Documentation. 2. Eva cannot handle Testing. 3. Alice and Bob must be adjacent in (Documentation → Deployment → Design → Testing). Based on the constraints, which statement MUST be true?
No valid schedule found given the constraints. The only guaranteed assignment is: David must handle Documentation.
If the constraints cannot all be satisfied, fallback is to force rule 1's assignment.
multi-person, shift-scheduling, constraint-satisfaction, puzzle

Question 2

Four team members (Eva, David, Charlie, Alice) must be assigned to four unique tasks (Deployment, Testing, Documentation, Design). The assignments must follow these rules: 1. Eva must handle Deployment. 2. David cannot handle Design. 3. Charlie and Alice must be adjacent in (Deployment → Testing → Documentation → Design). Based on the constraints, which statement MUST be true?
No valid schedule found given the constraints. The only guaranteed assignment is: Eva must handle Deployment.
If the constraints cannot all be satisfied, fallback is to force rule 1's assignment.
multi-person, shift-scheduling, constraint-satisfaction, puzzle

Question 3

Round Robin scheduling with time quantum = 3: - P1: Burst time 14 - P2: Burst time 5 - P3: Burst time 5 - P4: Burst time 10 - P5: Burst time 6 What is the average completion time?
Step-by-step solution:

1. Round Robin simulation:
2. Completion times:
- P2: 20
- P3: 22
- P5: 28
- P4: 38
- P1: 40

3. Average: 148 ÷ 5 = 29.6

Answer: 29.6
preemptive, interruptible, round-robin, OS, computer-science

Question 4

Four team members (Bob, Charlie, David, Alice) must be assigned to four unique tasks (Testing, Deployment, Documentation, Design). The assignments must follow these rules: 1. Bob must handle Testing. 2. Charlie cannot handle Design. 3. David and Alice must be adjacent in (Testing → Deployment → Documentation → Design). Based on the constraints, which statement MUST be true?
No valid schedule found given the constraints. The only guaranteed assignment is: Bob must handle Testing.
If the constraints cannot all be satisfied, fallback is to force rule 1's assignment.
multi-person, shift-scheduling, constraint-satisfaction, puzzle

Question 5

A production line needs to manufacture: - Product A: 1 units (each takes 1 hours) - Product C: 2 units (each takes 3 hours) - Product B: 2 units (each takes 1 hours) - Product D: 1 units (each takes 2 hours) Setup time required when switching products: - P->P: 1 hour What is the minimum total time if production starts with Product D?
Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product A: 1 x 1 = 1 hours
- Product C: 2 x 3 = 6 hours
- Product B: 2 x 1 = 2 hours
- Product D: 1 x 2 = 2 hours
- Base production time: 11 hours

2. Minimize setup time by batching:
- Optimal sequence: Product D -> Product A -> Product C -> Product C -> Product B -> Product B
3. Total with setups:
- Product D: 2 hours
- Setup Product D→Product A: 1 hour + Product A: 1 hours
- Setup Product A→Product C: 1 hour + Product C: 3 hours
- Product C: 3 hours (no setup)
- Setup Product C→Product B: 1 hour + Product B: 1 hours
- Product B: 1 hours (no setup)

Total: 14 hours

Key Strategy: Batch identical products together to minimize setup changes.
manufacturing, setup-time, sequencing, optimization

Question 6

Four colleagues need to schedule a meeting. Their available time slots are: - Alex: 9:00 AM, 10:00 AM, 2:00 PM, 3:00 PM - Ben: 10:00 AM, 11:00 AM, 2:00 PM - Cara: 9:00 AM, 11:00 AM, 12:00 PM, 3:00 PM - Diana: 10:00 AM, 12:00 PM, 2:00 PM, 3:00 PM What is the earliest time slot when all four can meet?
Step-by-step solution:

Set Intersection Method:
1. List all availability:
- Alex: {9:00 AM, 10:00 AM, 2:00 PM, 3:00 PM}
- Ben: {10:00 AM, 11:00 AM, 2:00 PM}
- Cara: {9:00 AM, 11:00 AM, 12:00 PM, 3:00 PM}
- Diana: {10:00 AM, 12:00 PM, 2:00 PM, 3:00 PM}

2. Find common slots (intersection):
- Common to all = Alex AND Ben AND Cara AND Diana
- Result: Empty set (No common time)

3. Conclusion: No common time slot available

Key Strategy: Use set intersection to find common availability, then choose the earliest time.
multi-person, time-slots, availability

Question 7

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 1 - Assemble: 45 min on Line 3 - Package: 15 min on Line 3 **Product Y:** - Cut: 20 min on Line 1 - Assemble: 60 min on Line 2 - Package: 20 min on Line 2 **Product Z:** - Cut: 40 min on Line 2 - Assemble: 30 min on Line 3 - Package: 25 min on Line 1 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 75 minutes
- Line 2: 120 minutes
- Line 3: 90 minutes

2. Identify bottleneck: The line with maximum load = Line 2
3. Bottleneck load: 120 minutes

Answer: Line 2 (120 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.
nested, bottleneck, resource-allocation, multi-line, factory

Question 8

In a single-elimination knockout tournament with 8 teams, how many total matches are played to determine the champion?
Step-by-step solution:

1. Single elimination principle: Each match eliminates exactly one team
2. Teams to eliminate: 8 - 1 = 7 teams must be eliminated
3. Matches needed: 7 matches

Answer: 7 matches
tournament, bracket, knockout, sports, competitive-exams

Question 9

A school needs to schedule 6 courses. The following courses have overlapping students and cannot be scheduled at the same time: - Chemistry conflicts with CS - Chemistry conflicts with Math - Chemistry conflicts with History - CS conflicts with Math - CS conflicts with Physics - CS conflicts with English - CS conflicts with History - English conflicts with Math - English conflicts with Physics - English conflicts with History - Math conflicts with History - Math conflicts with Physics What is the minimum number of time slots needed to schedule all courses without conflicts?
Step-by-step solution (Graph Coloring):

1. Model as graph coloring problem:
- Vertices = Courses
- Edges = Conflicts (courses that cannot be together)
2. Apply greedy coloring algorithm:
- Chemistry: Slot 1
- CS: Slot 2
- English: Slot 1
- Math: Slot 3
- History: Slot 4
- Physics: Slot 5

3. Colors/slots used: 5

Answer: Minimum 5 time slots

Key Strategy: The chromatic number of the conflict graph gives the minimum slots needed.
timetable, conflict-resolution, graph-theory, chromatic-number, advanced

Question 10

Four tasks (Task 4, Task 1, Task 3, Task 2) must be scheduled with these constraints: 1. Task 4 must be before Task 1 2. Task 1 must be before Task 3 3. Task 4 must be before Task 3 4. Task 2 must be after Task 3 Which constraint is REDUNDANT (does not add new information beyond the others)?
Step-by-step solution (Redundancy Detection):

1. List all constraints:
1. Task 4 must be before Task 1
2. Task 1 must be before Task 3
3. Task 4 must be before Task 3
4. Task 2 must be after Task 3

2. Check for transitive relationships:
- From Constraint 1: Task 4 before Task 1
- From Constraint 2: Task 1 before Task 3
- By transitivity: Task 4 before Task 3
- This makes Constraint 3 unnecessary (redundant)

3. Verify other constraints are independent:
- Constraint 4 (Task 2 after Task 3) adds unique information

Answer: Constraint 3 is redundant

Key Strategy: Look for transitive relationships (A→B, B→C implies A→C).
redundancy, logic, transitivity, critical-thinking, optimization

Question 11

Arrange the following activities in chronological order: Office Work, Evening Walk, Lunch Break, Dinner
Step-by-step solution:

Timeline Approach:
1. Convert all times to 24-hour format for easy comparison
- Office Work: 9:00 AM
- Evening Walk: 6:00 PM
- Lunch Break: 1:00 PM
- Dinner: 8:00 PM

2. Arrange in chronological order:
1. Lunch Break at 1:00 PM
2. Evening Walk at 6:00 PM
3. Dinner at 8:00 PM
4. Office Work at 9:00 AM

Final Schedule: Lunch Break -> Evening Walk -> Dinner -> Office Work

Key Strategy: Convert all times to 24-hour format and arrange from earliest to latest.
daily, time-based, chronological

Question 12

A hospital needs one doctor on-call each day for 30 days. There are 4 doctors: Dr. Smith, Dr. Patel, Dr. Jones, Dr. Lee. If the schedule is as fair as possible, how many days will each doctor be on-call?
Step-by-step solution:

1. Total on-call days: 30
2. Base days per doctor: 30 ÷ 4 = 7 days
3. Remainder: 2 doctor(s) get one extra day

Answer: 7 days, with 2 doctor(s) getting 8 days
on-call, availability, emergency, medical, fairness

Question 13

Hospital OR scheduling with 3 operating rooms (8 hours each): - Emergency: 41 min, Priority 1 - Urgent: 63 min, Priority 2 - Elective A: 65 min, Priority 3 - Elective B: 91 min, Priority 3 - Routine: 93 min, Priority 4 Can all surgeries be completed in one day?
Step-by-step solution:

1. Total surgery time: 353 min = 5.9 hours
2. Available OR hours: 3 × 8 = 24 hours
3. Total ≤ Available → Can complete in one day

Answer: All surgeries can be scheduled within one day
surgery, operating-room, hospital, healthcare, critical

Question 14

An event runs for 4 hours. Staff needed per hour: - Hour 1: 4 - Hour 2: 4 - Hour 3: 12 (PEAK) - Hour 4: 5 What is the minimum number of staff needed if staff can work multiple consecutive hours?
Step-by-step solution:

1. Identify peak demand: 12 staff at hour 3
2. Staff can work multiple hours → schedule around peak
3. Minimum staff needed: 12

Answer: 12 staff
event, staff, venue, hospitality, logistics

Question 15

In a round-robin tournament with 10 teams, each round consists of disjoint matches (no team plays twice in a round). What is the minimum number of rounds needed?
Step-by-step solution:

1. **Model as edge coloring of complete graph K_10
2. Vizing's theorem: χ'(K_n) = n-1 for even n, n for odd n
3. For 10 teams: 9 colors/rounds needed

Answer: 9 rounds
edge-coloring, match-scheduling, graph-theory, advanced, olympiad

Question 16

A production line needs to manufacture: - Product C: 3 units (each takes 3 hours) - Product B: 1 units (each takes 3 hours) - Product A: 1 units (each takes 4 hours) - Product D: 3 units (each takes 4 hours) Setup time required when switching products: - P->P: 3 hour What is the minimum total time if production starts with Product A?
Step-by-step solution:

Production Sequencing with Setup Times:
1. Calculate total production time (without setup):
- Product C: 3 x 3 = 9 hours
- Product B: 1 x 3 = 3 hours
- Product A: 1 x 4 = 4 hours
- Product D: 3 x 4 = 12 hours
- Base production time: 28 hours

2. Minimize setup time by batching:
- Optimal sequence: Product A -> Product C -> Product C -> Product C -> Product B -> Product D -> Product D -> Product D
3. Total with setups:
- Product A: 4 hours
- Setup Product A→Product C: 3 hour + Product C: 3 hours
- Product C: 3 hours (no setup)
- Product C: 3 hours (no setup)
- Setup Product C→Product B: 3 hour + Product B: 3 hours
- Setup Product B→Product D: 3 hour + Product D: 4 hours
- Product D: 4 hours (no setup)
- Product D: 4 hours (no setup)

Total: 37 hours

Key Strategy: Batch identical products together to minimize setup changes.
manufacturing, setup-time, sequencing, optimization

Question 17

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: - Prof. Garcia can only speak at 11:00-12:00 - Robotics and Cybersecurity cannot be in the same time slot - Dr. Lee and Dr. Chen must speak in consecutive time slots - AI Ethics must be in Hall C Which speaker presents the Machine Learning session?
Step-by-step solution:

Scheduling Grid Analysis:
1. Fix direct constraints:
- Prof. Garcia at 11:00-12:00
- AI Ethics in Hall C
2. Apply consecutive constraint: Dr. Lee and Dr. Chen in consecutive slots
3. Apply conflict constraint: Robotics and Cybersecurity not together

4. Final Schedule:
9:00-10:00:
- Hall A: Cybersecurity by Dr. Lee
- Hall B: Robotics by Prof. Wilson
- Hall C: AI Ethics by Dr. Chen
10:00-11:00:
- Hall A: IoT by Dr. Smith
- Hall B: (empty)
- Hall C: (empty)
11:00-12:00:
- Hall A: (empty)
- Hall B: (empty)
- Hall C: Machine Learning by Prof. Garcia

Answer: Prof. Garcia presents Machine Learning

Key Strategy: Use a grid to solve the assignment problem and satisfy all constraints sequentially.
multi-constraint, professional, CSP, CAT-level

Question 18

A company has 4 employees working in 3 shifts. Shifts rotate every 5 days. After how many days does an employee return to the same shift pattern?
Step-by-step solution:

1. Rotation cycle: 4 employees × 5 days = 20 days
2. Verification: Each employee cycles through all shifts

Answer: 20 days
rotation, cyclic, shift-pattern, workforce, healthcare

Question 19

A JIT manufacturing system has 4 jobs with the following data: | Job | Processing (min) | Due Date (min) | Early Penalty/min | Late Penalty/min | |-----|-----------------|----------------|-------------------|------------------| | Component B | 38 | 102 | 4 | 19 | | Component D | 57 | 116 | 3 | 14 | | Component A | 35 | 87 | 4 | 10 | | Component C | 35 | 45 | 1 | 15 | Using the Earliest Due Date (EDD) sequencing rule, what is the total penalty incurred?
Step-by-step solution (JIT Penalty Calculation):

1. EDD Sequence: Component C → Component A → Component B → Component D
2. Calculate completion times and penalties:
- Component C: completes at 35, due 45, early by 10 min → penalty 10
- Component A: completes at 70, due 87, early by 17 min → penalty 68
- Component B: completes at 108, due 102, late by 6 min → penalty 114
- Component D: completes at 165, due 116, late by 49 min → penalty 686

3. Total penalty: 878

Answer: 878 penalty points

Key Strategy: JIT scheduling minimizes total earliness + tardiness penalties, balancing inventory costs and customer satisfaction.
JIT, earliness, tardiness, penalty, inventory, lean-manufacturing

Question 20

A student has 6 days to prepare for three exams: Physics, Chemistry, Computer Science. The required preparation days are: - Physics: 2 days - Chemistry: 2 days - Computer Science: 1 days If the student follows the optimal schedule starting today, on which day will the last exam be?
Step-by-step solution:

Timeline Planning Method:
1. Calculate total preparation time needed:
- Physics: 2 days
- Chemistry: 2 days
- Computer Science: 1 days
- Total: 5 days

2. Available days: 6 days
3. Extra buffer days: 1 days
4. Optimal schedule:
- Days 1-2: Prepare for Physics
- Day 3: Physics exam
- Days 4-5: Prepare for Chemistry
- Day 6: Chemistry exam
- Days 7-7: Prepare for Computer Science
- Day 8: Computer Science exam

Answer: The last exam will be on Day 6

Key Strategy: Schedule exams immediately after preparation period ends, accounting for all required prep days.
academic, deadline, preparation, timeline
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