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Interval Graph Scheduling Beginner-Intermediate Worksheet: Focus on common variations practice Interval Graph Scheduling BEGINNER INTERMEDIATE

Level up your Interval Graph Scheduling skills! You're at Worksheet 4 of 10 (33% through this series). This step-up challenge worksheet features 20 beginner-intermediate-level problems with a focus on common variations practice. Topics covered: interval graph scheduling for competitive exams, how to solve interval graph scheduling, interval graph scheduling tricks.

📝 Worksheet 4 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner Intermediate level

What you'll learn in this worksheet:
Your progress through Interval Graph Scheduling
Worksheet 4 of 10 (33% complete)

Question 1

Events need to be scheduled in rooms. Their time intervals are: - Event A: 5:00 to 9:00 - Event B: 11:00 to 19:00 - Event C: 8:00 to 10:00 - Event D: 0:00 to 3:00 - Event E: 6:00 to 7:00 - Event F: 3:00 to 6:00 - Event G: 8:00 to 13:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: ████ from 5 to 9
Event B: ████████ from 11 to 19
Event C: ██ from 8 to 10
Event D: ███ from 0 to 3
Event E: █ from 6 to 7
Event F: ███ from 3 to 6
Event G: █████ from 8 to 13

2. Find maximum overlap:
Maximum 3 events overlap at once

Answer: 3 rooms needed

Question 2

Events need to be scheduled in rooms. Their time intervals are: - Event A: 15:00 to 16:00 - Event B: 17:00 to 23:00 - Event C: 1:00 to 4:00 - Event D: 20:00 to 28:00 - Event E: 19:00 to 26:00 - Event F: 4:00 to 11:00 - Event G: 4:00 to 12:00 - Event H: 6:00 to 7:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: █ from 15 to 16
Event B: ██████ from 17 to 23
Event C: ███ from 1 to 4
Event D: ████████ from 20 to 28
Event E: ███████ from 19 to 26
Event F: ███████ from 4 to 11
Event G: ████████ from 4 to 12
Event H: █ from 6 to 7

2. Find maximum overlap:
Maximum 3 events overlap at once

Answer: 3 rooms needed

Question 3

Events need to be scheduled in rooms. Their time intervals are: - Event A: 10:00 to 17:00 - Event B: 10:00 to 14:00 - Event C: 8:00 to 12:00 - Event D: 11:00 to 15:00 - Event E: 7:00 to 11:00 - Event F: 3:00 to 7:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: ███████ from 10 to 17
Event B: ████ from 10 to 14
Event C: ████ from 8 to 12
Event D: ████ from 11 to 15
Event E: ████ from 7 to 11
Event F: ████ from 3 to 7

2. Find maximum overlap:
Maximum 5 events overlap at once

Answer: 5 rooms needed

Question 4

Events need to be scheduled in rooms. Their time intervals are: - Event A: 18:00 to 21:00 - Event B: 6:00 to 14:00 - Event C: 8:00 to 16:00 - Event D: 14:00 to 19:00 - Event E: 19:00 to 20:00 - Event F: 19:00 to 24:00 - Event G: 9:00 to 11:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: ███ from 18 to 21
Event B: ████████ from 6 to 14
Event C: ████████ from 8 to 16
Event D: █████ from 14 to 19
Event E: █ from 19 to 20
Event F: █████ from 19 to 24
Event G: ██ from 9 to 11

2. Find maximum overlap:
Maximum 4 events overlap at once

Answer: 4 rooms needed

Question 5

Events need to be scheduled in rooms. Their time intervals are: - Event A: 13:00 to 16:00 - Event B: 2:00 to 7:00 - Event C: 12:00 to 15:00 - Event D: 15:00 to 19:00 - Event E: 2:00 to 9:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: ███ from 13 to 16
Event B: █████ from 2 to 7
Event C: ███ from 12 to 15
Event D: ████ from 15 to 19
Event E: ███████ from 2 to 9

2. Find maximum overlap:
Maximum 3 events overlap at once

Answer: 3 rooms needed

Question 6

Events need to be scheduled in rooms. Their time intervals are: - Event A: 0:00 to 3:00 - Event B: 16:00 to 17:00 - Event C: 6:00 to 11:00 - Event D: 10:00 to 15:00 - Event E: 17:00 to 19:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: ███ from 0 to 3
Event B: █ from 16 to 17
Event C: █████ from 6 to 11
Event D: █████ from 10 to 15
Event E: ██ from 17 to 19

2. Find maximum overlap:
Maximum 2 events overlap at once

Answer: 2 rooms needed

Question 7

Events need to be scheduled in rooms. Their time intervals are: - Event A: 18:00 to 22:00 - Event B: 19:00 to 22:00 - Event C: 15:00 to 22:00 - Event D: 5:00 to 12:00 - Event E: 8:00 to 14:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: ████ from 18 to 22
Event B: ███ from 19 to 22
Event C: ███████ from 15 to 22
Event D: ███████ from 5 to 12
Event E: ██████ from 8 to 14

2. Find maximum overlap:
Maximum 3 events overlap at once

Answer: 3 rooms needed

Question 8

Events need to be scheduled in rooms. Their time intervals are: - Event A: 6:00 to 7:00 - Event B: 13:00 to 14:00 - Event C: 7:00 to 8:00 - Event D: 8:00 to 16:00 - Event E: 15:00 to 20:00 - Event F: 5:00 to 8:00 - Event G: 2:00 to 8:00 - Event H: 16:00 to 19:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: █ from 6 to 7
Event B: █ from 13 to 14
Event C: █ from 7 to 8
Event D: ████████ from 8 to 16
Event E: █████ from 15 to 20
Event F: ███ from 5 to 8
Event G: ██████ from 2 to 8
Event H: ███ from 16 to 19

2. Find maximum overlap:
Maximum 4 events overlap at once

Answer: 4 rooms needed

Question 9

Events need to be scheduled in rooms. Their time intervals are: - Event A: 19:00 to 22:00 - Event B: 0:00 to 5:00 - Event C: 10:00 to 18:00 - Event D: 11:00 to 17:00 - Event E: 0:00 to 4:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: ███ from 19 to 22
Event B: █████ from 0 to 5
Event C: ████████ from 10 to 18
Event D: ██████ from 11 to 17
Event E: ████ from 0 to 4

2. Find maximum overlap:
Maximum 2 events overlap at once

Answer: 2 rooms needed

Question 10

Events need to be scheduled in rooms. Their time intervals are: - Event A: 10:00 to 11:00 - Event B: 19:00 to 22:00 - Event C: 2:00 to 7:00 - Event D: 0:00 to 7:00 - Event E: 17:00 to 20:00 - Event F: 15:00 to 20:00 - Event G: 1:00 to 6:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: █ from 10 to 11
Event B: ███ from 19 to 22
Event C: █████ from 2 to 7
Event D: ███████ from 0 to 7
Event E: ███ from 17 to 20
Event F: █████ from 15 to 20
Event G: █████ from 1 to 6

2. Find maximum overlap:
Maximum 3 events overlap at once

Answer: 3 rooms needed

Question 11

Events need to be scheduled in rooms. Their time intervals are: - Event A: 4:00 to 7:00 - Event B: 9:00 to 11:00 - Event C: 17:00 to 19:00 - Event D: 5:00 to 9:00 - Event E: 20:00 to 22:00 - Event F: 13:00 to 16:00 - Event G: 0:00 to 7:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: ███ from 4 to 7
Event B: ██ from 9 to 11
Event C: ██ from 17 to 19
Event D: ████ from 5 to 9
Event E: ██ from 20 to 22
Event F: ███ from 13 to 16
Event G: ███████ from 0 to 7

2. Find maximum overlap:
Maximum 3 events overlap at once

Answer: 3 rooms needed

Question 12

Events need to be scheduled in rooms. Their time intervals are: - Event A: 4:00 to 6:00 - Event B: 15:00 to 21:00 - Event C: 17:00 to 22:00 - Event D: 6:00 to 12:00 - Event E: 6:00 to 13:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: ██ from 4 to 6
Event B: ██████ from 15 to 21
Event C: █████ from 17 to 22
Event D: ██████ from 6 to 12
Event E: ███████ from 6 to 13

2. Find maximum overlap:
Maximum 3 events overlap at once

Answer: 3 rooms needed

Question 13

Events need to be scheduled in rooms. Their time intervals are: - Event A: 7:00 to 8:00 - Event B: 0:00 to 4:00 - Event C: 3:00 to 5:00 - Event D: 8:00 to 10:00 - Event E: 10:00 to 13:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: █ from 7 to 8
Event B: ████ from 0 to 4
Event C: ██ from 3 to 5
Event D: ██ from 8 to 10
Event E: ███ from 10 to 13

2. Find maximum overlap:
Maximum 2 events overlap at once

Answer: 2 rooms needed

Question 14

Events need to be scheduled in rooms. Their time intervals are: - Event A: 13:00 to 16:00 - Event B: 14:00 to 22:00 - Event C: 3:00 to 11:00 - Event D: 13:00 to 14:00 - Event E: 13:00 to 18:00 - Event F: 2:00 to 7:00 - Event G: 16:00 to 22:00 - Event H: 5:00 to 6:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: ███ from 13 to 16
Event B: ████████ from 14 to 22
Event C: ████████ from 3 to 11
Event D: █ from 13 to 14
Event E: █████ from 13 to 18
Event F: █████ from 2 to 7
Event G: ██████ from 16 to 22
Event H: █ from 5 to 6

2. Find maximum overlap:
Maximum 4 events overlap at once

Answer: 4 rooms needed

Question 15

Events need to be scheduled in rooms. Their time intervals are: - Event A: 4:00 to 12:00 - Event B: 13:00 to 20:00 - Event C: 4:00 to 5:00 - Event D: 14:00 to 19:00 - Event E: 19:00 to 25:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: ████████ from 4 to 12
Event B: ███████ from 13 to 20
Event C: █ from 4 to 5
Event D: █████ from 14 to 19
Event E: ██████ from 19 to 25

2. Find maximum overlap:
Maximum 3 events overlap at once

Answer: 3 rooms needed

Question 16

Events need to be scheduled in rooms. Their time intervals are: - Event A: 8:00 to 16:00 - Event B: 13:00 to 20:00 - Event C: 14:00 to 19:00 - Event D: 13:00 to 20:00 - Event E: 8:00 to 14:00 - Event F: 6:00 to 9:00 - Event G: 8:00 to 15:00 - Event H: 11:00 to 18:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: ████████ from 8 to 16
Event B: ███████ from 13 to 20
Event C: █████ from 14 to 19
Event D: ███████ from 13 to 20
Event E: ██████ from 8 to 14
Event F: ███ from 6 to 9
Event G: ███████ from 8 to 15
Event H: ███████ from 11 to 18

2. Find maximum overlap:
Maximum 7 events overlap at once

Answer: 7 rooms needed

Question 17

Events need to be scheduled in rooms. Their time intervals are: - Event A: 17:00 to 23:00 - Event B: 2:00 to 5:00 - Event C: 10:00 to 15:00 - Event D: 5:00 to 8:00 - Event E: 4:00 to 9:00 - Event F: 20:00 to 25:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: ██████ from 17 to 23
Event B: ███ from 2 to 5
Event C: █████ from 10 to 15
Event D: ███ from 5 to 8
Event E: █████ from 4 to 9
Event F: █████ from 20 to 25

2. Find maximum overlap:
Maximum 3 events overlap at once

Answer: 3 rooms needed

Question 18

Events need to be scheduled in rooms. Their time intervals are: - Event A: 9:00 to 13:00 - Event B: 9:00 to 14:00 - Event C: 11:00 to 17:00 - Event D: 13:00 to 18:00 - Event E: 13:00 to 19:00 - Event F: 14:00 to 20:00 - Event G: 20:00 to 28:00 - Event H: 10:00 to 11:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: ████ from 9 to 13
Event B: █████ from 9 to 14
Event C: ██████ from 11 to 17
Event D: █████ from 13 to 18
Event E: ██████ from 13 to 19
Event F: ██████ from 14 to 20
Event G: ████████ from 20 to 28
Event H: █ from 10 to 11

2. Find maximum overlap:
Maximum 5 events overlap at once

Answer: 5 rooms needed

Question 19

Events need to be scheduled in rooms. Their time intervals are: - Event A: 20:00 to 23:00 - Event B: 12:00 to 20:00 - Event C: 5:00 to 9:00 - Event D: 17:00 to 23:00 - Event E: 7:00 to 9:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: ███ from 20 to 23
Event B: ████████ from 12 to 20
Event C: ████ from 5 to 9
Event D: ██████ from 17 to 23
Event E: ██ from 7 to 9

2. Find maximum overlap:
Maximum 3 events overlap at once

Answer: 3 rooms needed

Question 20

Events need to be scheduled in rooms. Their time intervals are: - Event A: 15:00 to 21:00 - Event B: 10:00 to 17:00 - Event C: 18:00 to 19:00 - Event D: 11:00 to 16:00 - Event E: 19:00 to 27:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: ██████ from 15 to 21
Event B: ███████ from 10 to 17
Event C: █ from 18 to 19
Event D: █████ from 11 to 16
Event E: ████████ from 19 to 27

2. Find maximum overlap:
Maximum 3 events overlap at once

Answer: 3 rooms needed
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