Pigeonhole principle made easy

Solutions to 3 typical exam questions. See my other videos

[melm]

Thanks! I'm taking a combinatorics class and this video was very straightforward and easy to understand.

[drumroll]

Regarding the last one, I finally understood it when I thought about each handshake quantity as a "bucket" in which a person can fall. Because a quantity of 0 handshakes and a quantity of n-1 handshakes are mutually exclusive, that reduces the number of buckets to 4 (from what would have been 5). Now that there are less buckets than individuals at the meeting, the Pigeonhole Principle applies. Hope that helps someone.

[itsbeiko]

i learn so much more visually with the illustrations. it makes so much sense. 2 of the questions you put up are in my hw and it definitely helped me a lot!

[rapid]

The only video I found with an easy explanation.Thanks.

[AhmedOmar-ufgu]

This really helped me understand my Discrete Math Homework problems. Thank you.

[suticenmanda]

Cool video but just wondering something. Which accent it is? It is US English but which state or city? Can you tell me?

[andreaklempay]

yeah it's the first day of the semester and mah good ol advanced geometry teacher throws this at us and I'm like... yeah imma need a little bit more clarification. thx m8

[inaccessiblecardinal]

Fun! I really thought I'd see the one where among 6 people, it's always true that 3 are mutual strangers or 3 are mutual acquaintances. A good first step is PHP.

Not helping me with the damn Erdos-Rado partition theorems though.

[sagarmukherjee]

your videos are really good try and make some more on theory of numbers or discrete mathematics ...keep up the good work mate

[jongmagee]

This didn't make anything easier for me.

Its such a simple concept but people use such complicated examples to do so.

[nationalsecurityagency]

This is a very helpful explanation of a concept that's often over-complicated by textbooks. I found this when looking for KhanAcademy videos, but this explanation is easily as good as Khan's math videos. Great job! I think this channel will succeed.

[sudoku]

How did you prove the last one? I understand what you explain, but i dont get how you prove it with php.

[neettim]

It makes sense, thank you for the examples. However, I just don't get the concept of why it works by just having more "pigeons" than "holes" and then simply applying the Pigeon Hole Principle. I know the video is titled, "made easy", but do you have a more in-depth video explaining how the PHP works? 

[nourbenhadjsalem]

How can we respond to how many people must be gathered in a room to be sure that at least 4 are born in April?

[onesixeightpointonenine]

I was a little slow getting the first example. For other people having trouble with it: The five boxes with two numbers contain all the numbers. But we can only choose 1 number from each box, because if we choose two numbers from the same box, they will sum to 15. Since there is no 6th box, we will have to draw one of our numbers from the same box as another. i.e. We will have to choose two numbers that sum together to 15. So there is no way to both choose six of the numbers and not choose a pair that sum to 15.

Second example, not sure why the distance from one corner of a square to the other being sqrt(2) means that we can't fit 10 dots.

[hkgwei]

my 12 year old son has just studied this, and seems to enjoy and understand it. Are there any books you could recommend for someone of his age and ability? to give you an example he was able to answer this. Find the minimum number of positive integers to be written to ensure that there are two numbers such that there sum or difference is a multiple of 1378.
should I be looking for books introducing pure maths?
thanks

[apascoooal]

Nice video! Do u have videos that could help me with abstract algebra?

[mubasshiramomi]

could you please explain the last problem?
when n-1 people shake hands among n people then how could be it is at least two, I wanna know the fact without proofs

[shahishresth]

What's the answer of second part question
Is it 90 or something else

[inelify]

Second problem: why not just put 9points very close to each other and the last point as far away from them as possible? That would surely make two point more than sqrt(2) apart?