IMO 2024 Problem 1 (Explain it Like I'm 12)

IMO 2024 Problem 1: This video gives an explanation of how to approach this Olympiad problem by trying examples, noticing patterns then constructing a proof based on observations from the examples.

[decare]

I like how you walk us through the problem solving instead of just explaining the solution.

[abrarsays]

Loved it to the fullest. The way you explained felt so relaxing. Keep uploading ❤

[ultrio]

Oh my God

WHY is the solution this simple
I spent like 80 minutes trying to evaluate the right hand side for any alpha 😭😭😭

This makes me feel like I could've found the solution myself had I just spent a _little_ more time on it, thank you for the video

(P. S. for all the Ultrio finders, if you don't know what an ultrio finder is don't worry about it, and if you do well done you deserve an ultrio star)

[AdamJackson-kfeg]

Thank you for this accessible explanation to the problem, it is really appreciated! 😊 olympiad practise is always my go to for relaxing with all my stressful school coursework at the moment!!

[MuhammadDaniyal-uu]

I love your work (esecially the way of your explaination)... Please don't stop this great job!!!

[Lionking-lbgw]

i suggest putting videos with jee advanced math type problems title, your potential viewers will rise exponentialy, you can watch other youtube channels for thumbnail inspiration

[ctoko]

I have a similar solution containing even numbers but it's a little bit different.
Consider alpha = 2m + d where m is an integers and d is a floating part from the interval [0, 1/n) (excluding 1/n ) why doesn't this work as if d is less than 1/n
n×d <0 and when applying the floor it gets removed and we're left with the sum of even integers 2m that is a multiple of n as proved in this video. If you can please answer me and thanks in advance

[awkwardhamster]

i loved how u explained the problem ! Pls post more about often ! :)

[puppyfat]

I feel like there is a modular arithmetic proof in here somewhere. My first intuition was only even numbers for obvious reasons and then for any non integer it couldn’t possibly work for all n because you’re taking all factors.

I really have no way of explaining why that obviously means it cannot work though.

[tenkey]

I solved it by parts : 1st i supposed α€Z and found α=2β, 2nd i supposed α is rational . And i used strong induction by setting α=m/k
I checked for m=1 and then i continued the proof . And then in R it's easier since in Q there's no solutions .and in R it's in between the numbers so it doesn't take a lot to prove . Is it correct ??

[cirrus]

this might be the first time i understood a youtube math video 💀

[hasanjakir]

I thought for a while and found that even numbers work and odd numbers do not. My intuition was tellimg me tgere are no.more solutions, but I coupd not say how.

[mostafakarim]

Perfect solution👌❣️.. but lhave a a question..?

when alpha= n + 1/n

We have
Sum(n alpa)=
=sum(n²)+n = n(n+1)(2n+1)/6+n

[hafizzuddinnur]

So the answer would be just alpha is an even number, 'coz fraction would have some countermeasure (?), I'm a bit confused sorry for my lack of understanding 😅