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 9×9 grid with 3×3 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 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.
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.
But Shiga does make good comics. As for his maths past, it certainly shows in some of his work.
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.
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.
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.
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.
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.
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?
2 hasn't been solved, but looks okay-ish.
Why not have a go? If anyone can solve this, I'll be willing to reward you with something pointless and insignificant. Have fun!
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.
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.
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?
Today is Michaelmas. Hurrah for unknown Christian festivals.
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?
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?
Ever felt a little too happy? Here's the cure.