Practice - Tutorial 6: Part II
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Practice Questions
Test your understanding with targeted questions
What is the midpoint of points (2, 4) and (4, 8)?
💡 Hint: Use the midpoint formula: ((x1+x2)/2, (y1+y2)/2).
Choose any three integers from 1 to 8 and see if you can find at least one pair whose sum equals 9.
💡 Hint: Look for combinations that add up to 9.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does the pigeonhole principle state?
💡 Hint: Think about objects in boxes.
True or False: If two points have even coordinates, their midpoint will also have even coordinates.
💡 Hint: Calculate to check the conclusion.
3 more questions available
Challenge Problems
Push your limits with advanced challenges
Using the pigeonhole principle, prove that if there are 10 students in a class with 4 different hair colors, there is at least one color shared by at least three students.
💡 Hint: Think about distributing more items across fewer categories.
Show that among any ten integers selected from 1 to 20, there must be a pair whose sum is 21.
💡 Hint: Count and see which pairs complete the set.
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Reference links
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