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June 13, 2005

Probability Puzzle Time!

Writing about web page http://www.gchq.gov.uk/recruitment/careers/math_apply.html

This puzzle from the GCHQ recruitment website has completely flummouxed me. I suspect there is some sort of general method to dealing with stuff like this, but I have no idea what it is.

2. Alice and Bob play coin toss: Alice pays Bob £1 for each head and Bob pays Alice £1 for each tail they throw. They continue playing until one player loses (runs out of money). Initially Alice has £6 and Bob has £14.

a. Determine, with proof, the probability that Alice loses.
b. Determine the probability that Alice loses but also has at some time previously been within £1 of winning.


May 31, 2005

Sudoko Problem SOLVED!

Follow-up to Unsolved Problems In Mathematics #2242 : The Secret of Sudoku from The Militant Wing of Pacifism

Well, the number of solutions problem has been solved. I can't claim any credit, of course, but plenty of kudos for this Felgenhauer guy.

The number of valid Sudoku solution grids for the standard 99 grid with 33 regions was calculated by Bertram Felgenhauer to be 6,670,903,752,021,072,936,960 This number is equivalent to 9! 722 27 27,704,267,971, the last factor of which is prime.

Still awaiting confirmation, of course, but it seems pretty sound.

The mechanics of the solution isn't terribly technical, though. Basically, it's a brute force search by computer for unique solutions, which we then multiply by the appropiate number of symmetries. (From above, 27,704,267,971 are the unique solutions, and the rest we multiply by are symmetries.)

The code used is available here. It's in C++ and python, so you should be able to test it yourself. The solution was found based on discussions on an internet forum, so obviously these things are useful, after all!

The minimum givens problem is still open, though.


May 28, 2005

Fleep, the comic

Writing about web page http://www.shigabooks.com/shigabooks/csfolder/fleep.html

Jason Shiga majored in Maths. So, kids, you might see this as a sort of inspiration about what to do with your maths degree. I mean, how to be rich and successful and stuff.

Jason Shiga now works in a library. Ok, scratch that about inspiration…

But Shiga does make good comics. As for his maths past, it certainly shows in some of his work.

Like Fleep, for example

Fleep about a guy who gets trapped in a phone booth. A phone booth, that has suddenly and inexplicably become surrounded by concrete. All the words around him appear to have turned to gibberish, and all he has with him are the phone, a phonebook he can't read, a few coins, a pen, a book in Russian, and a note which he also can't read. Plus, he's running out of air.

He's also extremely smart. Can he escape? Can he figure out how he got trapped in the first place? Well, to say any more would be to spoil things.

Go. Read. Now.


May 22, 2005

Murder, he wrote

Writing about web page http://www.nydailynews.com//front/story/310320p-265498c.html

OK, I lied about being dead. Being dead helps me in my skulking-around-activities, so I can work on Project-Eliminate-My-Enemies. It's not like anyone even cared. Bastards.

But, ok, forgive me for the divergence.

Possibly the creepiest thing ever

A doomed Queens man's chilling computer entry led cops to a suspect who allegedly robbed and killed the victim and his sister to finance a return to China, police said yesterday.

So, this guy gets murdered. They catch the murderer, because just before that, he posted a blog entry wondering about his sister's weird boyfriend, who is hanging around his flat for apparently no reason. A short while after he posts his last entry, the boyfriend ties him up, and when he can't find any money, he stabs Simon Ng repeatedly in the chest. And then, a while later, Simon's sister Sharon comes back, and gets stabbed as well.

And the Blog is still up. Really, you can read it here.

And when you read it, it strikes you that the whole thing is completely normal. It's just the blog of a random, mundane, person. Half the articles are on stuff like I'm doing badly on on Japanese class, or about how much hard work it is to clean up. Stuff that we students can all connect to. And then, that final entry.

Today I missed my Japanese class again, since I have gotten a bad throat. I only went to the class once this week, so I am probably so far behind now. I will catch up in the summer tho so no worries hehe. Anyway today has been weird, at 3 some guy ringed the bell. I went down and recognized it was my sister's former boyfriend. He told me he wants to get his fishing poles back. I told him to wait downstair while I get them for him. While I was searching them, he is already in the house. He is still here right now, smoking, walking all around the house with his shoes on which btw I just washed the floor 2 days ago! Hopefully he will leave soon, oh yeah working on the jap report as we speak!

Just non-commital. Just another day. Worrying about homework. Concerned more about his floor, than feeling threatened.

And then he dies.


April 06, 2005

Tricky Puzzle of the Diagonal Tiles

A reasonably tough puzzle a friend of mine thought up: Which may well be insoluble, or may have been mentioned in some place already.

Consider a rectangular grid of arbitary size. Say, M by N grid squares, in size.

The grid is filled with tiles, each of them containing a 45 degree (or Pi/2 radian, for pure maths pedants) line segment – the line either goes from top right to bottom left, or top left to bottom right.

For example, below is a possible configuration:

Obviously, there are 2^(M*N) possible configurations. Now, what concerns us are the regions generated by the outer boundary of the grid and the diagonal tile lines. I.e. the red lines. Specifically, the number of distinct closed regions thus generated.

The Big Questions are:

1. What is the minimum number of regions for a given grid?
2. What is the maximum number of regions for a given grid?
3. Out of all the possible configurations, how is the region number distributed?

1 can be solved semi-easily. The answer is M + N regions. Proof is an exercise for the reader. (Think about the available length of outer-boundary available, and how much each external-touching region must use up)

2 hasn't been solved, but looks okay-ish.

3 is insanity itself.

Why not have a go? If anyone can solve this, I'll be willing to reward you with something pointless and insignificant. Have fun!


October 10, 2004

The Day of the Spam

Today will be recorded as the day I received the first piece of spam on my warwick email account.

This is bad. Very bad.

Because, as we all know, spammers pass on lists to each other. Thus, before long, every spammer in the world would have my email, and the deluge of spam will increase roughly exponentially. Worse, the University uses this email to contact me, so I'll end up having to wade in each day.

Gah!

I'm not entirely certain where they got the address from. Can they get emails off warwick blogs? My hope is that they are randomly guessing, and so may just give up.

On the bright side of things, I just got a GMail invite. Yay!

Spam levels in all my accounts:

Hotmail(1): 100/day. (I don't bother checking it. It's probably been deleted.)
Hotmail(2): 0. (I don't use this account any more. Just a login for MSN.)
Freeserve (1): 30/day
Freeserve (2): 50/day (I think I wrote some articles online in which I naively mentioned these addresses. BAD idea)
Polarisboard: 0. (I never use this account except for special stuff. )
Warwick: 1, so far.

What about you lot?

Site of the day is The Internet Mapping Project.

Just go and gawk.


October 04, 2004

Time to Traverse Those Twisty Little Passages…

Writing about web page http://ifcomp.org/

All modern IF authors may well hate me, now. (Mazes are deeply unfashionable, these days. ) And all non-IF players will be utterly confused.

Ok, you may be asking yourself this:

What is IF?

IF is short for Interactive Fiction.

Of course, that doesn't help. TV is, after all, interactive fiction, since you can switch the damn thing on or off, and change channels. A book in interactive fiction in that you can turn its pages, or if you are in certain loony fundamentalist sects (not that I am passing judgement, or anything…), toss into a burning pyre. Pornography, done well, is definitely interactive fiction. In fact, many of the best works of official 'IF' have succeeded in the remarkable act of being either uninteractive, or nonfictional.

Crazy people, eh?

Quite. Interactive fiction is really the new name for text adventure. After the commercial programmers finished with the medium, it ended up being taken up by a whole culture of hobbiests. And being mostly students, it was neccessary to add a new level of pretension to the proceedings. Suddenly, they weren't making games anymore, not least adventure games. They were making art.

But still, the basic medium has remained the same. In broad terms, then:

Interactive Fiction/Text Adventure describes a computer program which tells a story or simulates a scene by mainly ascii text, responding to commands given in the form of typed instructions from the user/player.

Maybe I've been a little too cynical.

Because, despite the protestations of the old nostalgics, the new stuff is quite good. Very good in fact, and often rivaling the old Infocom days in terms of quality. But the new works are different, and you need to play them with different expectations than when you play the older ones, or really, any sort of game.

An important list of points for new players.

1. Winning is not the point of IF.
While all games tend to have end points, the point of IF is the experience, not the destination. A good IF author accounts for unusual responses, and part of the fun is looking for them. You are deeply damaging your gameplay experience if you do not EXAMINE every item, person, animal, abstract entity etc.

2. The game is not real.
A counter to the previous, really. While IFs attempt to be 'real life', they are in the end simply computer programs. While you are quite free (in how many other types of game can you use the command SING?), you are ultimately constrained. Specifically, the instructions you enter need to be in the form: > VERB (OBJECT)

3. Do not expect.
IF is young, really young in the scheme of things. Much of it is experimental. There is a great chance of you finding something unexpected. Or an almighty bug. Try and play as many as you can.

4. If you are unhappy, complain.
Almost all IF is free, but current IF development works closely with those who play. (Especially since the community is so small that most players are authors.) If you have a problem, or a suggestion, ask in rec.games.int-fiction or rec.arts.int-fiction. But be nice.

So why am I talking about this now?

Because IFComp 2004 has just started. IFComp is a competition for IF, which happens annually and is judged by a public vote. That's right. You can go to the website right now, and download the games, play them, and submit a vote.

Do you have an excuse not to?


IFComp Website

Actually, maybe you do. Its a good idea to play a few 'classic' works first to get the hang of the engine. You can find some at:

Best of IF

And

Emily Short's IF Page

Hop to it!


September 29, 2004

Something Special

Writing about the 3th day in warwick from Ning's blog

Today was nothing special?

How can one say that? That something was not special? Even if a thing had no interesting characteristics about it, it would be deemed special because it turns out to be one of those rare things that is completely uninteresting.

But that is a moot point, because today is something special. Let's make a list. (This is really getting worrying now. I am making way too many lists. I need help. Please help me. Bleh. (What on earth does bleh mean? (Oh dear… I am also putting brackets inside brackets. This must be a bad thing.)))

  1. You exist today. Consider the length of the universal time – the universe has existed for over 12 Billion years, and will continue to exist perhaps indefinitely. The subset of days in which you exist is infinitessimal in porportion. And if humanity turns out to be the only conscious lifeform, then the significance becomes gargantuan.
  2. 153 thousand people died today. Ok, this figure is probably not very accurate, but consider the enormity of it. On newspapers, we see alot made of incidents like 9/11 in which a few thousand die. But the hidden figure is vast. This amounts to a huge untelevised global catastrophy almost all the time. The birth rate too, is similar. Does talk of daily specialness truly hold any significance next to it?
  3. Today is Michaelmas. Hurrah for unknown Christian festivals.
  4. Spaceship One launched successfully today, completing one half of the X-Prize. This may revolutionise public accessible space travel. This day may well be remembered…

Ok, I'm bored of this. The point is, specialness is there if you are willing to look for it. Doesn't that make you warm and fuzzy?

Now, for assorted news.

Student union elections due within a few days. I talked to some of my fellow freshers about it. Result? Zilch. No one had heard of anyone standing as councillor. Few had even heard that you can vote. In fact, barely anyone knows that the Student Union is in fact democratic. So what happens if less than the requisite number of people sign up as candidates? Dubya may well be taking notes.

I found out there are actually fiction books in the library. Wow! Not a big collection though, and most seem pretty well hidden. Does anyone else have any pointers?

Today's Link

Ever felt a little too happy? Here's the cure.


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