So Counting is Actually Pretty Hard

[@WrathofMath]

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[@IsaacDickinson-tf8sf]

A counting problem I’ve come back to when I get bored in the summer is the probability that when picking k dominos from a complete set of dominos with highest value l and lowest blank, that they will form a complete chain, in any order. I solved this for k=2 and possibly k=3 but k=4 and the general rule is still undetermined.

[@tomkerruish2982]

I don't know the answer, but I'd suggest modeling the set of dominoes as a graph, with each vertex being a particular domino and there being an edge between two vertices iff they can form part of a chain. You would then need to determine how many paths of length k-1 edges exist that do not pass through any vertex more than once. Of course, this might be what you've already done, in which case I have nothing to add.

[@GeraldPreston1]

I might be special because I can actually count with ease and I don't even need to use my fingers anymore. My mum said I'm very talented because I could count to 10 when I was only 7 years old

[@WrathofMath]

Yes youre very special 🤗

[@thiagogoncalves7389]

​@@WrathofMathOh he's "special" alright

[@angelicaesturban7777]

@@thiagogoncalves7389i like counting to 1024 with my fingers 😊

[@someperson188]

@0:46 The text under the second summation sign should be: 1

[@cloudyfromtpotreal]

i love how i watch these videos even though i dont understand anything and i dont even know my times tables

[@WrathofMath]

Maybe we need to do a times tables video. Hey, there's a hog video tomorrow, maybe you'll like that!

[@cloudyfromtpotreal]

@@WrathofMath we just did counting, so we should do addition next, maybe a series going up to like the tetration and stuff

[@talastra]

@@cloudyfromtpotreal there's a lot of ground between counting and addition. You could watch Wrath's earlier videos tho.

[@anthonycheng1765]

Inclusion-Exclusion Principle

[@WhatThePhi]

Solid vid brother, Keep it up!

[@WrathofMath]

Appreciate it!

[@thechallenger6124]

recently had to solve this in my code. was a doozie for anyone code related the easy way is a nested boolean only dict that holds the sports within the dict that holds the people. abuse array intersects to finish the job. very similar to this persons math.

[@denischen8196]

Given a number, if the number is odd, multiply it by 3 and add 1, if it is even, divide it by 2. Repeat until you reach 1. Is there an efficient way to count the number of iterations it will take to reach 1 for any given number?

[@styleurcam]

if there was, then the proof for the Collatz conjecture would have been found a while ago, but the Collatz conjecture wasn't proven or disproven, so there is no discovered formula for this

[@alexicon2006]

Nah there isnt a way to determine that. Since if we find the formula, then we can easily find which numbers, if any, wokld lie outside of this end result and the Collatz Conjecture will be solved. But we arent there yet.

[@xXJ4FARGAMERXx]

y'all are basically saying: we haven't found it, therefore, it doesn't exist Which is like, that's a cop-out Also, historically it's a 50:50 whether something you don't find exists or not "I haven't found my old phone for 5 years, therefore, it doesn't exist"

[@styleurcam]

@@xXJ4FARGAMERXx We're saying we haven't found an explicit formula, because if it had been found, the Collatz conjecture would be solved thanks to it. We're not saying an explicit formula doesn't exist, only that we haven't found it

[@talastra]

@@xXJ4FARGAMERXx Actually, it's not 50/50, because the proof may be true if you include some assumptions, false if not (in other words, proofs that are neither true nor false or both false and true) ... or it could be Godel incompleteness unprovable. However, It's 2 am; I'm not typing the thinks correctly.

[@leytonbennet2692]

I'm majoring in combinatorics at school right now and I have never seen that formula before in my life, definitely would have made things easier!

[@WrathofMath]

That's awesome (your major, not lack of seeing the formula)! Combinatorics is such a rich subject, I hope you enjoy your studies!

[@hillaryclinton1314]

3:28 i disagree with this method. After the first two 1:2 box, the winner moves to the 102 slot. After 3:4, - that winner moves to 103, 5:6 to 104... etc. 99:100 to 151..... The counter ends at 200. Divide by 2 per match..100 bouts..

[@EnthalpyUplusPV]

This is such a good video

[@WrathofMath]

Thank you!

[@robetheridge6999]

Well, I still only know this fundamental principle of enumberation in theory. It would be nice if you were to actually use that last problem to fill in the summation.

[@arlenestanton9955]

The summation, Greek symbol means to add, n=3

[@mousy9903]

12:49 how come they dont ALL play at least one of the two sports. If you play basketball thans at least one, and if you play both basketball and football that would be at least one sport. Maybe this might be a language thing, my being influenced by languages other than english mightve skewed my understanding, but doesnt at least one mean that you just need one, and anything else is disregarded as it is irrelevant?

[@WrathofMath]

They do all play at least one of the two sports, the difficulty is in counting how many is in "all" because of the overlap in the groups

[@michaeltherandomperson9652]

Till this day, I still suck at doing counting, lol. And then the professor gave us some of the really hard olympiad questions of counting and pigeonhole principle.

[@WrathofMath]

Haha yeah - math competitions are rife with combinatorics! They can quickly get way harder than you'd ever think when you first hear "counting problems"

[@tomasbeltran04050]

counting parts of math sometimes troubled me because the wording confused me 😢😢😢

[@royalroamer1]

the zelda music is such a W

[@WrathofMath]

timeless!

[@rewixx69420]

bro wtf is puiseux serise why dose it use newton polygons what magic is this

[@Dravignor]

Do a video on the Pigeonhole principle because funi name

[@WrathofMath]

Will do!

[@Dravignor]

Can't wait!

[@alexicon2006]

Pigeonhole Principle is like the Mean Inequality of Combinatorics, Probability and all the related spheres. Meaning it is one of the most unexpectedly useful principles out there. You see some advanced applications of it and you just wonder how one tool can be used in so many ways in so many places, just like QM>=AM>=GM>=HM Inequality.

[@CrashSable]

So less than 2 minutes in and it's already not about counting and the title is clickbait

[@lollol-tt3fx]

The only person counting is hard for is a mathmatician.

[@WrathofMath]

🤣🤣

[@alexicon2006]

Now thats a fact if Ive ever seen one

[@vampire_catgirl]

Dang it, I count like a machine TwT

[@WrathofMath]

hey, it's accurate!