Holy smokes this is amazing. This dude is a phenomenal lecturer! The sound levels are intense at times, but this lecturer and his lecture are of such high quality that I couldn't stop watching.
Conjecture: Every set of 2^{n-2} + 1 points in the plane in general position contains a subset of n points which form a convex n-gon. This is one of the most famous unsolved problems in combinatorial geometry, perhaps due in part to its lovely history. The problem of showing that every sufficiently large set of points in general position determine a convex n-gon was the original inspiration of Esther Klein. Erdös called this the Happy end problem since it led to the marriage of Esther Klein and George Szekeres. This problem was also one of the original sources of Ramsey Theory.
I liked this problem about self reproducing Kolakoski sequence 1,2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1,2,1,1,2,1,2,2,1,1 the density of 1s is 1/2, but this conjecture remains unproved and what is the nth term of this sequence
The notion of "family of sets" used in this conjecture does not allow copies of elements. Therefore in your example, you actually just consider two sets. I agree that it should have been stated more clearly by saying that these sets should be different since the usage of "family of sets" is different in some contexts.
Some problems cannot be solved at all. And not all problems are of the same difficulty. If your problem is how will America always be the 1st world superpower you might have an easy time. However if you 're facing a task that may take 1.000.000 years to complete well you are in for a hell of a time!
1-In fact there is NO set problem which cannot be solved through subset sum, subset integral and subset optimisation rules of synthetic analysis. The challenge is only in our current level of comprehending how to use it 2-
Holy smokes this is amazing. This dude is a phenomenal lecturer! The sound levels are intense at times, but this lecturer and his lecture are of such high quality that I couldn't stop watching.
Conjecture: Every set of 2^{n-2} + 1 points in the plane in general position contains a subset of n points which form a convex n-gon.
This is one of the most famous unsolved problems in combinatorial geometry, perhaps due in part to its lovely history. The problem of showing that every sufficiently large set of points in general position determine a convex n-gon was the original inspiration of Esther Klein. Erdös called this the Happy end problem since it led to the marriage of Esther Klein and George Szekeres. This problem was also one of the original sources of Ramsey Theory.
Amazing lecture. It was simply astounding to see this collection of conjectures. Even more so when they did not include the usual suspects
in 2014 Bousch proved that Frame-Stewart algorithm for solving 4-pegged Towers of Hanoi is indeed optimal. The paper is in french though.
Great talk but it's really unfortunate how the audio is clipped so badly. Whoever ran audio for this event did a disservice to the speaker.
What a treat it must been to be there. Really amazing to see the Master at work
fantastic lecturer and lecture!
HAVE YOU TRIED TURNING IT OFF, AND THEN TURNING IT BACK ON AGAIN?
❤
I liked this problem about self reproducing
Kolakoski sequence
1,2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1,2,1,1,2,1,2,2,1,1
the density of 1s is 1/2, but this conjecture remains unproved
and what is the nth term of this sequence
so i guess the first problem also assumes that each set is unique in the family of sets, otherwise the answer would be trivial
Maybe a 505. 504. Problem guessing.
Thankyou.
In the first problem, why can you not just have two empty sets and one set containing only one element as a counter example?
The notion of "family of sets" used in this conjecture does not allow copies of elements. Therefore in your example, you actually just consider two sets. I agree that it should have been stated more clearly by saying that these sets should be different since the usage of "family of sets" is different in some contexts.
Some problems cannot be solved at all. And not all problems are of the same difficulty. If your problem is how will America always be the 1st world superpower you might have an easy time. However if you 're facing a task that may take 1.000.000 years to complete well you are in for a hell of a time!
1-In fact there is NO set problem which cannot be solved through subset sum, subset integral and subset optimisation rules of synthetic analysis. The challenge is only in our current level of comprehending how to use it
2-
Thank goodness for our engineers
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