Solving An Insanely Hard Problem For High School Students

Olympiad problems are challenging for most of us. But this one was considered "easy" for the students taking the test! (The oldest students are in high school, but have also been 13 year old students who have taken the test and gotten a gold medal).

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[RedPig_Olympiad]

Hey Presh Talwalkar, very nice solution! I find your video extremely clear and well presented, I should better learn some presentation skill from you.
BTW, thank you for mentioning my channel, I really appreciate it. Cheers!

[loawtf]

the only thing I understood about this math video is that if there are 6 problems, and each one is worth 7 points, that there is a total of 42 possible points.

[RaVeN]

"You can pause the video to try yourself." Five weeks later:"Let's just continue the video."

[gandhimahatma]

I attended the IMO in high school cuz I thought I was good at math and scored a 0. Good times lol

[ZidaneTribal]

I don't even understand the question

[bjrnee]

i guess i couldnt even compete in the paralympics version of this

[locowachipanga]

It's pleasant to hear some honest words like "I couldn't solve it myself" instead of "This is how you proceed" Zero ego involved. I appreciate that.

[gustavobassani]

me after graduating in mathematics: well, i can solve any problem now.

me looking at a high school imo problem: well, better do a master's degree

[collin]

Pffft this question wasn't a challenge to me. I didn't even bother to try it and I knew I couldn't do it

[cartoon.raccoon]

as someone who’s been doing a lot of linear algebra lately, i immediately picked up on the fact that this equation very closely resembled the definition of linearity, (i.e. f(a) + f(b) = f(a+b) and f(ca) = cf(a)). then assuming f was linear, it was very easy to solve from there. i was just going off my intuition though, so your solution was probably much more rigorous and would certainly stand up better under scrutiny!

[robrazzano]

Okay...so 1 + b is the same as b + 1. Got that...


...gonna need you to slow down now.

[physicsguy]

When in doubt, plug in numbers. 1 and 0 usually work out nice.

[entropyss]

compared to what maths has been like for me in high school this is real maths, the maths at school feels like it lacks the aspect of researching and exploring solutions
when I watch your videos I learn how to approach problems, but I'm also stimulated

[sharpnova]

worth mentioning that though IMO contestants may have found this comparatively easy, they are constantly training and facing problems of this nature and these types of techniques. most of them will see this type of problem and have a lot to fall back on almost immediately.


source: am an IMO silver medalist

[tehArcher]

the interesting part was showing that the set of solutions had to be linear, actually from that point it was really straight forward

[eliasgonzalez]

He lost me at "let z be the set of integers"

[BilguunBatbayar]

Since the high school, the problem of problem solving for me was always understanding the problem.

[pb]

To people who feel bad for not finding it while its supposed to be "easy". Consider this, the people who do these olympiads have seen this type of question before. It's very often the same type of questions, and with the same way of solving them. You have to train for these olympiads and this type of question is a pretty common one

[asparkdeity]

4 years ago, I didn’t understand any of this. Now, studying maths at Uni, it’s so easy to follow

[sohn]

Viewers: “we want harder problems“
Presh:
Viewers:“surprised pikachu face“