Week 3: Want to win a million dollars?

To win the money, all you need to do is solve any one of the seven problems that, in an understatement comparable with 'Getting stung by a blue-bottle jellyfish is a little uncomfortable', make up my Problem of the week 3.

Those good guys over at the Clay Institute decided 5 years ago to offer a $1 million prize for solutions to any of seven particular unsolved mathematics problems, dubbed the millenium problems.

Official problem descriptions can be found here:
Birch and Swinnerton-Dyer Conjecture
Hodge Conjecture
Navier-Stokes Equations
P vs NP
Poincar� Conjecture
Riemann Hypothesis
Yang-Mills Theory

One catch though, according to the rules you will have to wait at least two years after submitting your solution before you can be eligible for the money (just to make sure it stands up to scrutiny).

Any takers?

Problem of the week #2

Well after a reasonable show of interest to problem of the week 1, of which the solution is now posted, this week it shall be an exercise in pure logic. Given the response to that Einstein riddle thing on the front nomadlife page a few weeks ago, I think we will all have more success with this one. It seems that the game of Sudoku has become quite popular recently in a few newspapers around the world, especially London, and so I've taken my problem from this game.

Basically the idea is this: You have a 9*9 grid, which is also divided up into nine 3*3 squares. The idea is to fill in all 81 squares so that every row, every column and each of the nine 3*3 squares all contain the digits 1 through 9. And no row, column or 3*3 square can use a digit twice. Some of the numbers are provided at the start, and these cannot be changed.

Again like last week I am posting an easy version and a hard version. Enjoy :)

The easy version:


The hard version:

Problem of the week #1

Okay, so recent observations have led me to the conclusion that the general level of logical and mathematical ability amongst nomadlifers needs some encouragement. And so I am starting up a problem of the week section, where you mathematicians out there can show off your prowess, and the rest of you can be further educated in this wonderful field (especially Luli, who I know just loves it when my blog postings get educational). I might even think of a prize to bestow upon those who contribute the best answers.

And so to kick things off, a quick dabble into geometry. What is the side length (or area, if you prefer to answer that way) of the largest equilateral triangle that can fit entirely inside a unit square?

And for the more adventurous, once you get past that one, try the same question but in 3 dimensions. (i.e. what is the side length of the largest regular tetrahedron that can fit inside a unit cube?)

Creativity is encouraged.

3 months already

So, I have now been living in Bogot� for just over 3 months. The time seems to have gone very fast. My traineeship is for one year. That is already a quarter of the way gone. A year isn't as long as it used to be... (and to any pedants or people taking that comment literally who want to point out how silly that last comment is, I suggest you study astronomy a bit more, and you might find that I am right in a literal sense too.)

The weather in Bogot� is really stange. Melbourne is famous in Australia for having 4 seasons in one day, but in Melbourne's case it is an exaggeration. But in Bogot�, it is a fair observation, and holds true for alomst every day. Yesterday had beautiful bright sunshine and warmth, cold winds, dry grey cloudy skies, rain, and even a bit of hail, all in one day. It does rain a lot here at this time of year (ie daily), but the good thing is it's a pretty safe bet that if you simply wait an hour, the rain will have stopped. Which is good, because right now it is lunch time, and yet it is raining. I hope it stops soon.