Mathematics in Chutes and Ladders



From Wikipedia:

Any version of Snakes and Ladders can be represented exactly as a Markov chain, since from any square the odds of moving to any other square are fixed and independent of any previous game history. The Milton Bradley version of Chutes and Ladders has 100 squares, with 19 chutes and ladders. A player will need an average of 39.6 spins to move from the starting point, which is off the board, to square 100.

In the book Winning Ways the authors show how to treat Snakes and Ladders as a (loopy) impartial game in combinatorial game theory even though it is very far from a natural fit to this category.

The world’s 23 toughest math questions

From NetworkWorld.com:

Those wacky folks at he the Defense Advanced Research Projects Agency have put out a research request it calls Mathematical Challenges, that has the mighty goal of “dramatically revolutionizing mathematics and thereby strengthening DoD’s scientific and technological capabilities.”

The challenges are in fact 23 questions that if answered, would offer a high potential for major mathematical breakthroughs, DARPA said. So if you have ever wanted to settle the Riemann Hypothesis, which I won’t begin to describe but it is one of the great unanswered questions in math history, experts say. Or perhaps you’ve always had a theory about Dark Energy, which in a nutshell holds that the universe is ever-expanding, this may be your calling.

DARPA perhaps obviously states research grants will be awarded individually but doesn’t say how much they’d be worth. The agency does say you’d need to submit your research plan by Sept. 29, 2009.

So if you’re game, take your pick of the following questions and have at it.

(via Kottke)

Server Issues

Update 2:

(IGNORE the orange template. Just testing something

Currently have 3 support tickets open. Not a happy Dreamhost customer at the moment. Here’s what’s happened.

This blog has grown to the point where shared hosting is no longer a feasible option. On Friday, Dreamhost moved this site to a VPS with a scalable memory/processor option. Within 24 hours, I was maxed out at 2 Gigs of memory and the site was slow to the point where I could barely get on, nevermind update. I put in a support ticket and I got a quick response saying:

If you like I can try installing our process watcher (it runs on shared
hosting machines and will kill runaway processes you have). Bear in mind
though it’s not a fix (really you would want to find and disable
inefficient code or any loops you have that might be causing the resource
usage).

Since sending them an email to tell them to start the process watcher, the memory usage has doubled (before that it was using a measly 1.2Gigs of mem) and I’ve deactivated all wordpress plugins. I’ve sent in two more support tickets asking for help in trying to isolate what is causing all the memory usage and so far have received no help from them. My patience is starting to wear thin with their support. I’m currently looking for other hosting, dedicated or vps but I’m still concerned with the amount of memory being used by wordpress. It’s possible that there’s some rogue script that’s eating memory and perhaps a brand new install would work but I’m hoping to get some support from Dreamhost before I make that move.

If anybody has any suggestions, similar experiences, or Zoloft, send me an email at cc@cynical-c.com (email hasn’t had any problems).

Update:

Still having major problems with the site slowing down or not working at all. I’m trying to resolve it through my current host but I have the suspicion that the problem is that this blog has just outgrown what my current host (Dreamhost) is able to handle. If anybody has any suggestions for dedicated hosting that can handle a wordpress blog that gets over 10,000 hits a day, please email me at cc@cynical-c.com.

I’m having some problems with the server. I have a support ticket open and hopefully it’s only a minor hiccup.

Big Difference in Chinese vs English Math Tests

From BBC News:

Maths enthusiasts are being challenged to answer a sample question from Chinese university entrance tests.

The tests are set for prospective science undergraduates.

The UK’s Royal Society of Chemistry is offering a £500 prize to one lucky but bright person who answers the question below correctly.

It has also published a test used in a “well known and respected” English university – the society is not naming it – to assess the strength of incoming science undergraduates’ maths skills.

A glance at the two questions reveals how much more advanced is the maths teaching in China, where children learn the subject up to the age of 18, the society says.

Science undergraduates in England are likely not to have studied maths beyond GCSE level at the age of 16, it says.

(via Reddit)

Calculating the Value of Prostitution

From The Guardian:

[(δU/δL) / (δU/δC) | Sp=0] ≤ w – [(δU/δr) / (δU/δC) | S = 0]

U is your satisfaction. It’s what you, as a prostitute, care about – the satisfaction you gain from selling your services. Economists like to call it “utility”, which is why they like to use the letter “U”.

L is the amount of leisure you have.

C is the amount of goods and services you, as a consumer, consume.

S is the amount of prostitution you, as a prostitute, sell to your customers.

W is the going price for prostitutes.

R is a measure of your reputation.

(via Cosmic Variance)

How to Calculate Pi by Throwing Frozen Hot Dogs

From WikiHow:

Believe it or not, of all the countless ways to approximate the most prolific irrational number in the universe, there are none quite as interesting or as surprisingly satisfying as throwing perfectly good food around your kitchen. In fewer steps than it takes to circumscribe your house in a circle of baguettes, you, too, can easily add a slice of pi into your dinner menu tonight. The best part is…it really works!

(via Information Junk)