An interesting proof of Menger's theorem

The proof is in

The Hahn-Banach theorem, Menger’s theorem, and Helly’s theorem

from What's New (Terrence Tao's blog).

I subscribed to his blog a while ago, but most of the time I have to skip his posts as I don't really understand the title.. but this one is of some interest to me as I did some study in graph theory this summer and used Menger's theorem in a proof.

In his post, Terrence has given a new proof to Menger's theorem by using a game-theoretic argument. I still need to spend more time later to understand the details, but this idea again, shows the beauty and unity of mathematics!

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Life is an opportunity to do something.

An interesting probabiilty problem

Toss a fair coin n times, what is the probability of having at least k consecutive Heads (i.e., we could have more than k consecutive Heads).

The problem looks simple but once you tried it, you will find that it is not very easy. It is a very good test for your understanding on Probability :), so I strongly encourage you to have a try! And you may encounter this in an interview!

I will try to post the solution later, if I can solve it.
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Life is an opportunity to do something.