I'm thinking of a number...

Here is a game. You are presented with countably infinitely many boxes. Each containing a single real number, you're allowed to open as many boxes as you like and view the number inside the now opened box. However to end this game you need at some point in time to point to a specific box and before opening it guess the number inside it. Due to horribly unimaginative rules, you win if you guess right and lose if you guess wrong.

At first glance this seems like a game you're bound to lose all the time. However if you arm yourself with the axiom of choice it is possible to win with large probability. Your challenge is to find the optimal solution.

Hat tip to Zach Hamaker for showing me this problem which I believe originally comes from his advisor Peter Winkler

Proofs from the book

I came across a really nice thread on Quora today. It asks about the most beautiful proofs in mathematics.

Alot of people gave alot of really nice answers. The thread is here. Anyone have any other good ones?

Really really ridiculously cute

Apologies to Zoolander for the title. But if you're feeling down about the various things to feel down about in the world, then  Cuteoverload is really cute and cheer uppy.

Just a cool link today.

Ever wonder how many people are in space? At time of writing 3
http://www.howmanypeopleareinspacerightnow.com/

A puzzle of primes

This is a fairly old one I first saw in a high school, at one of the Stellenbosch university olympiad camps.  Enjoy.

It's possible to find a string of 1000 consecutive integers with no primes. For example
1001!+2,1001!+3,...,1001!+1001. Does there exist a string of consecutive integers with exactly 5 primes?

Another powers of two post

I've been negelectign this blog of late.
To keep the posts flowing here is one of the internets great time sinkers.

Odin takes quizzo way too seriously

Recently I've  reread parts of Tales of the Norsemen by Roger Lancelyn Green. Who does an excellent job of describing various mythologies (there is a series).  Anyway one of the myths described is of Odin and the wise giant Valfthrudnir having a "quiz to the death".  As described in the link they agree to ask each other questions until someone gets one wrong and then the winner cuts off the loser's head and keeps it.

I've got a question about this. First up how do they decide weather a particular question is right assuming they disagree? In this tale they don't but what exactly stops a conversation like this happening?

Valf: Which Stallion draws the chariot of the moon?
Odin: It's called "Milky".
Valf: No it's called "Snowy" I get your head!!
Odin: No I'm pretty sure it's "Milky" so I get your head.
Valf: SNOWY!!!!!!
Odin: MILKY!!!!!!!!!

How do they go about judging this?