• CKSTEM
  • Learn 
    • CKSTEM Courses
    • New Year, New Dreams, New Successes!
    • CKSTEM Family Challenges
    • Holiday Fun Activities
    • How to Outsmart AI?
    • Doses of Motivation
    • Talent V/S Core Values
    • Problem Solving Strategies
  • Compete 
    • Canadian Innovation Contests
    • Australian Mathematics Contest 2025
    • TIMO
    • BBB Olympiad
    • HKIMO
  • Win 
    • Contest Winners
    • CIC 2024 Winners
    • CIC 2023 Winners
    • CIC 2022 Winners
  • Team 
    • About Us
    • Executives
  • …  
    • CKSTEM
    • Learn 
      • CKSTEM Courses
      • New Year, New Dreams, New Successes!
      • CKSTEM Family Challenges
      • Holiday Fun Activities
      • How to Outsmart AI?
      • Doses of Motivation
      • Talent V/S Core Values
      • Problem Solving Strategies
    • Compete 
      • Canadian Innovation Contests
      • Australian Mathematics Contest 2025
      • TIMO
      • BBB Olympiad
      • HKIMO
    • Win 
      • Contest Winners
      • CIC 2024 Winners
      • CIC 2023 Winners
      • CIC 2022 Winners
    • Team 
      • About Us
      • Executives
broken image
broken image
broken image
  • CKSTEM
  • Learn 
    • CKSTEM Courses
    • New Year, New Dreams, New Successes!
    • CKSTEM Family Challenges
    • Holiday Fun Activities
    • How to Outsmart AI?
    • Doses of Motivation
    • Talent V/S Core Values
    • Problem Solving Strategies
  • Compete 
    • Canadian Innovation Contests
    • Australian Mathematics Contest 2025
    • TIMO
    • BBB Olympiad
    • HKIMO
  • Win 
    • Contest Winners
    • CIC 2024 Winners
    • CIC 2023 Winners
    • CIC 2022 Winners
  • Team 
    • About Us
    • Executives
  • …  
    • CKSTEM
    • Learn 
      • CKSTEM Courses
      • New Year, New Dreams, New Successes!
      • CKSTEM Family Challenges
      • Holiday Fun Activities
      • How to Outsmart AI?
      • Doses of Motivation
      • Talent V/S Core Values
      • Problem Solving Strategies
    • Compete 
      • Canadian Innovation Contests
      • Australian Mathematics Contest 2025
      • TIMO
      • BBB Olympiad
      • HKIMO
    • Win 
      • Contest Winners
      • CIC 2024 Winners
      • CIC 2023 Winners
      • CIC 2022 Winners
    • Team 
      • About Us
      • Executives
  •  
  • Canadian Innovation Contests
    • CKSTEM
    • Learn 
      • CKSTEM Courses
      • New Year, New Dreams, New Successes!
      • CKSTEM Family Challenges
      • Holiday Fun Activities
      • How to Outsmart AI?
      • Doses of Motivation
      • Talent V/S Core Values
      • Problem Solving Strategies
    • Compete 
      • Canadian Innovation Contests
      • Australian Mathematics Contest 2025
      • TIMO
      • BBB Olympiad
      • HKIMO
    • Win 
      • Contest Winners
      • CIC 2024 Winners
      • CIC 2023 Winners
      • CIC 2022 Winners
    • Team 
      • About Us
      • Executives
    • …  
      • CKSTEM
      • Learn 
        • CKSTEM Courses
        • New Year, New Dreams, New Successes!
        • CKSTEM Family Challenges
        • Holiday Fun Activities
        • How to Outsmart AI?
        • Doses of Motivation
        • Talent V/S Core Values
        • Problem Solving Strategies
      • Compete 
        • Canadian Innovation Contests
        • Australian Mathematics Contest 2025
        • TIMO
        • BBB Olympiad
        • HKIMO
      • Win 
        • Contest Winners
        • CIC 2024 Winners
        • CIC 2023 Winners
        • CIC 2022 Winners
      • Team 
        • About Us
        • Executives
    broken image
    broken image
    broken image
    • CKSTEM
    • Learn 
      • CKSTEM Courses
      • New Year, New Dreams, New Successes!
      • CKSTEM Family Challenges
      • Holiday Fun Activities
      • How to Outsmart AI?
      • Doses of Motivation
      • Talent V/S Core Values
      • Problem Solving Strategies
    • Compete 
      • Canadian Innovation Contests
      • Australian Mathematics Contest 2025
      • TIMO
      • BBB Olympiad
      • HKIMO
    • Win 
      • Contest Winners
      • CIC 2024 Winners
      • CIC 2023 Winners
      • CIC 2022 Winners
    • Team 
      • About Us
      • Executives
    • …  
      • CKSTEM
      • Learn 
        • CKSTEM Courses
        • New Year, New Dreams, New Successes!
        • CKSTEM Family Challenges
        • Holiday Fun Activities
        • How to Outsmart AI?
        • Doses of Motivation
        • Talent V/S Core Values
        • Problem Solving Strategies
      • Compete 
        • Canadian Innovation Contests
        • Australian Mathematics Contest 2025
        • TIMO
        • BBB Olympiad
        • HKIMO
      • Win 
        • Contest Winners
        • CIC 2024 Winners
        • CIC 2023 Winners
        • CIC 2022 Winners
      • Team 
        • About Us
        • Executives
    •  
    • Canadian Innovation Contests
      broken image
      • CKSTEM
      • Learn
        • CKSTEM Courses
        • New Year, New Dreams, New Successes!
        • CKSTEM Family Challenges
        • Holiday Fun Activities
        • How to Outsmart AI?
        • Doses of Motivation
        • Talent V/S Core Values
        • Problem Solving Strategies
      • Compete
        • Canadian Innovation Contests
        • Australian Mathematics Contest 2025
        • TIMO
        • BBB Olympiad
        • HKIMO
      • Win
        • Contest Winners
        • CIC 2024 Winners
        • CIC 2023 Winners
        • CIC 2022 Winners
      • Team
        • About Us
        • Executives
      • Canadian Innovation Contests

        Why Can't We Make Exactly 7 Friends?

        Proof by the students for the question in newsletter

        April 15, 2021 · Math-In-Action,Learn By Proofs,POTW

        We asked to provide a proof for the following problem in our last newsletter. We are publishing the best explained response. Lookout for our future newsletter. Your response can also be published. It's important to continue to learn by proofs.

        Prove that we can't make exactly 7 friends

        “CKSTEM has 25 students in a class, and each student is friends with exactly seven classmates.” Why can’t that statement be true?

        Why Can't We Make Exactly 7 Friends?

        Proof BY Ansh Agarwal

        First, let’s assume that each student can make friends with 7 students. If each student puts a checkmark in their notebook for each friend they have, there would be 7 checkmarks for each student, and 7 * 25 = 175 checkmarks in total. Now, let’s look at what happens when 2 students become friends. Each person puts a checkmark in their book, so the total amount of checkmarks goes up by 2. Since the total amount of checkmarks starts at 0, the total amount of checkmarks is always even. Since we got an odd number, our previous assumption was false, and so, it is not possible to have 25 students in a class, where everyone is friends with 7 students.

        Why Can't We Make Exactly 7 Friends?

        We can generalize our observation. If class size is 25 (odd) then all students can't have equal but odd number of friends, however, it's possible to have have equal but even number of friends for all students.

        What happens if a class has even number of students? You know how to put checkmarks in your notebooks - right? It's your turn to analyze this situation. Understanding parity (odd and even) can help you in solving many cool problems.

        Thanks Ansh Agarwal for sending us a creative proof. You can learn more about Ansh here. You can also add your comments if you have additional thoughts on proving this.

        CKSTEM SUMMER CONTEST REFERRAL PROGRAM

        You can help your friends by asking them to join CKSTEM contests. If they enter your name while signing up then you will be eligible for a lucky draw. You will have one entry for each referral. You will not only help your friends to be a part of the most amazing contests, you may also win some cool prizes.

        Help Your Friends! CKSTEM Contest Referral Program!
        Help Your Friends

        ABOUT THE COMPETITIVE KIDS STEM

        CKSTEM is a volunteer-run, nonprofit organization engaged in enhancing kids' education and enabling them to achieve excellence. We focus on teaching problem solving and enabling critical thinking by 'connecting the dots' as well as developing mental dexterity for the students.

        We believe that in order to grow, students need to develop beyond their comfort zone, so we ensure they are consistently and appropriately challenged. We not only coach them to understand and problem solve but also train them to compete, nurturing their competitive spirit and mental fitness, similar to competitive sports. ​

        Previous Newsletter: Formula for Student's Success!

        Subscribe
        Previous
        Using Triangle Inequalities
        Next
        Learn To Be A Great Problem Solver!
         Return to site
        ×
        Store Categories
          Cookie Use
          We use cookies to improve browsing experience, security, and data collection. By accepting, you agree to the use of cookies for advertising and analytics. You can change your cookie settings at any time. Learn More
          Accept all
          Settings
          Decline All
          Cookie Settings
          Necessary Cookies
          These cookies enable core functionality such as security, network management, and accessibility. These cookies can’t be switched off.
          Analytics Cookies
          These cookies help us better understand how visitors interact with our website and help us discover errors.
          Preferences Cookies
          These cookies allow the website to remember choices you've made to provide enhanced functionality and personalization.
          Save