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  • Dec 31, 2014

  • We introduce the pigeonhole principle, an important proof technique. #DiscreteMath #Mathematics #Proofs #Pigeonhole Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW Like us on Facebook: http://on.fb.me/1vWwDRc Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.


  • John Smith
    John Smith 4 years ago

    i have 0 friends

  • WeKnowJoey
    WeKnowJoey 3 years ago


  • Omkar S
    Omkar S 4 years ago

    "No! Everybody has a friend here." You're so inspirational :,)

  • FifthDoctorsCelery
    FifthDoctorsCelery 4 years ago

    The friends one still works if you allow people to have 0 friends. Then people can have {0, ..., n-1} friends. From here, either two people have the same number of friends (so the proof is done), or each person has a different number, which means there is one person in each box. However, this is a contradiction, because it says that one person has 0 friends and one has n-1 (the maximum number, since you can't be friends with yourself). It's impossible to have one friendless person and one who is friends with everybody, so either there is nobody in the friendless box or there is nobody in the n-1 box. Either way, there are now n-1 total boxes for n people, so two people must share a box.

  • MeRaKi DaY1
    MeRaKi DaY1 2 years ago

    "Maybe one of them is a serial killer" lol

  • Rajendra Kumar Dangwal

    Hey TrevTheTutor

  • ghty102
    ghty102 4 years ago


  • Lucy Novacka
    Lucy Novacka 4 years ago

    Good explanation of this easy-difficult concept. Many thanks :)

  • Haomin Tian
    Haomin Tian 2 years ago

    Hi, I love your videos! And really appreciate! I have a question here that I am not sure if I should use Pigeonhole Principle:

  • Kaushik Donthi
    Kaushik Donthi 1 year ago (edited)

    Okay, I have a question on the last problem - I am getting that you can at most have only 13 dots that are at most sqrt(8) away from each other at the same time. Your idea of 16 that you can have 1 dot on each square is not correct, I feel! If I could send you a picture, I would but it seems that adjacent diagonals reuse the same diagonals

  • M.
    M. 4 years ago

    hi Trevor I have a discrete math final coming up soon do you have any tips/advice ?thank you!

  • Sora
    Sora 1 year ago

    I really really love you. You make my life so much easier. Thank you so much!

  • Raghav khanna
    Raghav khanna 5 months ago

    Two of the best teachers at YouTube you and organic chemistry tutor

  • sup
    sup 6 months ago

    one question i would like you to explain is

  • Jonnathan Nickolai
    Jonnathan Nickolai 4 years ago

    awesome video ! just a side note, if it's a leap year it could be the case that 2 people do not have the same birthday.

  • M. Syahman Samhan
    M. Syahman Samhan 4 years ago

    beautiful. thanks a lot :)

  • Adarsh Nathaniel
    Adarsh Nathaniel 11 months ago

    Great way of teaching sir. I learnt this topic in just 20 min. Tysm.

  • Rita
    Rita 9 months ago

    this vid legit look like a troll for the first minute lmfao

  • madhusai vemulamada
    madhusai vemulamada 4 years ago

    no dislikes and that tells you how good you explain. really great explanation.

  • Karmanya GB
    Karmanya GB 3 years ago

    dude the first question aren't u supposed to mention that everyone has at least 1 friend