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Interval Graph Scheduling - Intermediate Level: tricky scenarios handling Interval Graph Scheduling INTERMEDIATE

This expert challenge 📈 worksheet focuses on Interval Graph Scheduling - a key topic in Scheduling. You'll solve 20 intermediate-level problems (Worksheet 5 of 10). The primary focus is on tricky scenarios handling. Master how to solve interval graph scheduling, interval graph scheduling tricks, and interval graph scheduling shortcut methods through systematic practice.

📝 Worksheet 5 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Interval Graph Scheduling
Worksheet 5 of 10 (44% complete)

Question 1

Events need to be scheduled in rooms. Their time intervals are: - Event A: 9:00 to 10:00 - Event B: 14:00 to 17:00 - Event C: 17:00 to 21:00 - Event D: 15:00 to 16:00 - Event E: 14:00 to 21:00 - Event F: 15:00 to 22:00 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 10
Event B: ███ from 14 to 17
Event C: ████ from 17 to 21
Event D: █ from 15 to 16
Event E: ███████ from 14 to 21
Event F: ███████ from 15 to 22

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

Answer: 4 rooms needed

Question 2

Events need to be scheduled in rooms. Their time intervals are: - Event A: 16:00 to 19:00 - Event B: 4:00 to 7:00 - Event C: 1:00 to 7:00 - Event D: 0:00 to 4:00 - Event E: 9:00 to 16:00 - Event F: 15:00 to 23:00 - Event G: 9:00 to 15:00 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 16 to 19
Event B: ███ from 4 to 7
Event C: ██████ from 1 to 7
Event D: ████ from 0 to 4
Event E: ███████ from 9 to 16
Event F: ████████ from 15 to 23
Event G: ██████ from 9 to 15

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: 13:00 to 15:00 - Event B: 18:00 to 26:00 - Event C: 5:00 to 10:00 - Event D: 4:00 to 10:00 - Event E: 7:00 to 9:00 - Event F: 13:00 to 15:00 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 15
Event B: ████████ from 18 to 26
Event C: █████ from 5 to 10
Event D: ██████ from 4 to 10
Event E: ██ from 7 to 9
Event F: ██ from 13 to 15

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

Answer: 3 rooms needed

Question 4

Events need to be scheduled in rooms. Their time intervals are: - Event A: 12:00 to 20:00 - Event B: 3:00 to 10:00 - Event C: 4:00 to 12:00 - Event D: 3:00 to 9:00 - Event E: 2:00 to 3:00 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 12 to 20
Event B: ███████ from 3 to 10
Event C: ████████ from 4 to 12
Event D: ██████ from 3 to 9
Event E: █ from 2 to 3

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

Answer: 3 rooms needed

Question 5

Events need to be scheduled in rooms. Their time intervals are: - Event A: 8:00 to 15:00 - Event B: 2:00 to 5:00 - Event C: 20:00 to 22:00 - Event D: 3:00 to 7:00 - Event E: 3:00 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 8 to 15
Event B: ███ from 2 to 5
Event C: ██ from 20 to 22
Event D: ████ from 3 to 7
Event E: ████████ from 3 to 11

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: 5:00 to 9:00 - Event B: 13:00 to 14:00 - Event C: 4:00 to 8:00 - Event D: 7:00 to 15:00 - Event E: 16:00 to 20:00 - Event F: 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 5 to 9
Event B: █ from 13 to 14
Event C: ████ from 4 to 8
Event D: ████████ from 7 to 15
Event E: ████ from 16 to 20
Event F: ███████ from 2 to 9

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

Answer: 4 rooms needed

Question 7

Events need to be scheduled in rooms. Their time intervals are: - Event A: 13:00 to 21:00 - Event B: 12:00 to 16:00 - Event C: 20:00 to 24:00 - Event D: 0:00 to 6:00 - Event E: 14:00 to 17:00 - Event F: 14:00 to 22:00 - Event G: 19:00 to 21:00 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 21
Event B: ████ from 12 to 16
Event C: ████ from 20 to 24
Event D: ██████ from 0 to 6
Event E: ███ from 14 to 17
Event F: ████████ from 14 to 22
Event G: ██ from 19 to 21

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

Answer: 4 rooms needed

Question 8

Events need to be scheduled in rooms. Their time intervals are: - Event A: 6:00 to 11:00 - Event B: 1:00 to 8:00 - Event C: 4:00 to 10:00 - Event D: 19:00 to 21:00 - Event E: 7:00 to 8:00 - Event F: 11:00 to 17:00 - Event G: 2:00 to 5:00 - 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 6 to 11
Event B: ███████ from 1 to 8
Event C: ██████ from 4 to 10
Event D: ██ from 19 to 21
Event E: █ from 7 to 8
Event F: ██████ from 11 to 17
Event G: ███ from 2 to 5
Event H: █ from 5 to 6

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: 18:00 to 20:00 - Event B: 19:00 to 27:00 - Event C: 11:00 to 19:00 - Event D: 12:00 to 19:00 - Event E: 2:00 to 7:00 - Event F: 15:00 to 18:00 - Event G: 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 18 to 20
Event B: ████████ from 19 to 27
Event C: ████████ from 11 to 19
Event D: ███████ from 12 to 19
Event E: █████ from 2 to 7
Event F: ███ from 15 to 18
Event G: ███ from 10 to 13

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

Answer: 4 rooms needed

Question 10

Events need to be scheduled in rooms. Their time intervals are: - Event A: 7:00 to 11:00 - Event B: 11:00 to 17:00 - Event C: 18:00 to 24:00 - Event D: 0:00 to 3:00 - Event E: 15:00 to 19:00 - Event F: 13:00 to 21:00 - Event G: 5:00 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 7 to 11
Event B: ██████ from 11 to 17
Event C: ██████ from 18 to 24
Event D: ███ from 0 to 3
Event E: ████ from 15 to 19
Event F: ████████ from 13 to 21
Event G: ██████ from 5 to 11

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: 12:00 to 15:00 - Event B: 10:00 to 12:00 - Event C: 5:00 to 9:00 - Event D: 3:00 to 6:00 - Event E: 2:00 to 8:00 - Event F: 14:00 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 12 to 15
Event B: ██ from 10 to 12
Event C: ████ from 5 to 9
Event D: ███ from 3 to 6
Event E: ██████ from 2 to 8
Event F: ████ from 14 to 18

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: 10:00 to 18:00 - Event B: 13:00 to 21:00 - Event C: 17:00 to 23:00 - Event D: 10:00 to 11:00 - Event E: 10:00 to 11:00 - Event F: 5:00 to 12:00 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 18
Event B: ████████ from 13 to 21
Event C: ██████ from 17 to 23
Event D: █ from 10 to 11
Event E: █ from 10 to 11
Event F: ███████ from 5 to 12

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

Answer: 4 rooms needed

Question 13

Events need to be scheduled in rooms. Their time intervals are: - Event A: 5:00 to 6:00 - Event B: 14:00 to 15:00 - Event C: 1:00 to 3:00 - Event D: 17:00 to 20:00 - Event E: 11:00 to 12:00 - Event F: 8:00 to 15:00 - Event G: 7:00 to 8:00 - Event H: 14:00 to 20:00 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 6
Event B: █ from 14 to 15
Event C: ██ from 1 to 3
Event D: ███ from 17 to 20
Event E: █ from 11 to 12
Event F: ███████ from 8 to 15
Event G: █ from 7 to 8
Event H: ██████ from 14 to 20

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

Answer: 3 rooms needed

Question 14

Events need to be scheduled in rooms. Their time intervals are: - Event A: 18:00 to 22:00 - Event B: 3:00 to 9:00 - Event C: 8:00 to 15:00 - Event D: 7:00 to 14:00 - Event E: 5:00 to 8:00 - Event F: 0:00 to 6:00 - Event G: 20:00 to 21:00 - Event H: 20:00 to 21:00 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 3 to 9
Event C: ███████ from 8 to 15
Event D: ███████ from 7 to 14
Event E: ███ from 5 to 8
Event F: ██████ from 0 to 6
Event G: █ from 20 to 21
Event H: █ from 20 to 21

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: 10:00 to 14:00 - Event B: 3:00 to 8:00 - Event C: 5:00 to 7:00 - Event D: 9:00 to 16:00 - Event E: 20:00 to 28:00 - Event F: 2:00 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 14
Event B: █████ from 3 to 8
Event C: ██ from 5 to 7
Event D: ███████ from 9 to 16
Event E: ████████ from 20 to 28
Event F: █████ from 2 to 7

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: 0:00 to 8:00 - Event B: 20:00 to 28:00 - Event C: 15:00 to 16:00 - Event D: 5:00 to 7:00 - Event E: 16:00 to 19:00 - Event F: 20:00 to 22:00 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 8
Event B: ████████ from 20 to 28
Event C: █ from 15 to 16
Event D: ██ from 5 to 7
Event E: ███ from 16 to 19
Event F: ██ from 20 to 22

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

Answer: 2 rooms needed

Question 17

Events need to be scheduled in rooms. Their time intervals are: - Event A: 14:00 to 15:00 - Event B: 9:00 to 13:00 - Event C: 6:00 to 13:00 - Event D: 1:00 to 4:00 - Event E: 4:00 to 7:00 - Event F: 9:00 to 14:00 - Event G: 15:00 to 16:00 - Event H: 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 14 to 15
Event B: ████ from 9 to 13
Event C: ███████ from 6 to 13
Event D: ███ from 1 to 4
Event E: ███ from 4 to 7
Event F: █████ from 9 to 14
Event G: █ from 15 to 16
Event H: ███ from 10 to 13

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

Answer: 4 rooms needed

Question 18

Events need to be scheduled in rooms. Their time intervals are: - Event A: 17:00 to 18:00 - Event B: 6:00 to 11:00 - Event C: 12:00 to 15:00 - Event D: 10:00 to 14:00 - Event E: 1:00 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 17 to 18
Event B: █████ from 6 to 11
Event C: ███ from 12 to 15
Event D: ████ from 10 to 14
Event E: ██████ from 1 to 7

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

Answer: 2 rooms needed

Question 19

Events need to be scheduled in rooms. Their time intervals are: - Event A: 11:00 to 16:00 - Event B: 0:00 to 1:00 - Event C: 3:00 to 6:00 - Event D: 10:00 to 18:00 - Event E: 1:00 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 11 to 16
Event B: █ from 0 to 1
Event C: ███ from 3 to 6
Event D: ████████ from 10 to 18
Event E: ██████ from 1 to 7

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

Answer: 2 rooms needed

Question 20

Events need to be scheduled in rooms. Their time intervals are: - Event A: 12:00 to 20:00 - Event B: 14:00 to 16:00 - Event C: 19:00 to 23:00 - Event D: 16:00 to 20:00 - Event E: 8:00 to 16:00 - Event F: 15:00 to 23:00 - Event G: 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 12 to 20
Event B: ██ from 14 to 16
Event C: ████ from 19 to 23
Event D: ████ from 16 to 20
Event E: ████████ from 8 to 16
Event F: ████████ from 15 to 23
Event G: ██████ from 19 to 25

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

Answer: 5 rooms needed
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