Discrete Math - 6.2.2 A Pigeonhole Proof

Your textbook does a great job of taking you through several "more elegant" applications of the Pigeonhole Principle. In this video, I take you through one that isn't showcased in your textbook in proving that 9 ordered triples must have at least one pair that have integer midpoints.

Video Chapters:
Intro 0:00
Setting up the Proof 0:31
The Proof 6:18
Up Next 11:10

[corneliswiredu]

Thanks madam, keep us going. You're actually helping we the computer science students in the university of capecoast, keep it up.

[TinyMaths]

To be fair, at first glance, I got that 'terrified' feeling of "what on Earth is this question even about?"
But after calming down and letting the initial panic subside, and reading through it slowly, thinking about what all the notation actually means, it made more sense than I imagined.
This was always a significant problem for me; that initial knee-jerk moment that seems to cause the 'deer in headlights effect'. I'm still out of college at the moment, but when I was in I was definitely guilty as charged for having that reaction and zoning out; and yes, I zoned out on the pigeon-hole principle which is why I decided to watch when I saw your vid. Thanks.

[toasteduranium]

I found that getting ahead on mathematics is too hard, but spreading my net wide is very easy. So, instead of learning the contents of my class ahead of time, I’m just learning the content of math classes I don’t have ahead of time.

[darcash]

2|(2k-2m), 2|(2k+1 - (2m-1)), so as long as they match even/odd, the midpoint on each axis will E Z.
The num of partitions is the same for each axis: 2. So total partitions = 2^3 = 8.

n = 9 (object num)
p = 8 (partitions)
ceil(9/8) = 2, so that checks out

[dreamworld]

A class has 40 students, aged 16 to 38 years old. You want to guarantee that the class

contains at least x students of the same age. What is the largest x can be?

[KunthShah]

what is the textbook referred in this video?

[shayorshayorshayor]

All that just to find that k is 8 and N is 9?