This blog has been moved to:  http://algebrahut.com/blog/

Thank you to everyone who has visited my blog.  Please continue to do so in the future at the above address.

~The Witch Doctor

I finally took the leap.  I signed up for a domain (algebrahut.com) and webhosting services (bluehost) just a few days ago.  You can even visit www.algebrahut.com, though there is not much to do there just yet.  It is going to be a massive work in progress for some time to come.  I have all these ideas I want to explore, but I’m having to tell myself just to focus on a couple of ideas with an end in sight.

I am hosting algebrahut.com via bluehost.  After signing up, they gave me a call to confirm.  I wasn’t available, so they left a message.  I haven’t returned the call, but that’s good customer service on their part.

I had been researching the concepts I had in mind for my site and found that much of it seemed over my head.  However, once I ‘got my hands dirty’ with it, everything I had read made much more sense.  In one day, I was able to set up a Moodle account and, on a seperate day, a phpbb3 forum that renders math using mimetex. 

To my surprise, phpbb3 allows buttons (bbcode) that type in all the code using shorthand and inserts it in the post, so the user doesn’t have to know all the mess of code that goes into rendering the math images.  I want to change the text on the button, an option not immediately available in the phpbb3 software.  I went to view the code through bluehost’s cpanel, but my computer froze up at the over 1000 lines of code.  I’ll have to try it again.  Ultimately, I want to have a math forum that makes typing the math almost as easy as typing words, where the math looks like the way it is written by hand.  Again, a work in progress.

Bluehost has made setting up Moodle and the phpbb3 forum a cinch.  I’m sure doing it manually would have been much more challenging.  Bluehost has this program called cpanel, within which there is fantastico deluxe, which makes the installation of Moodle and phpbb3 as simple as a few mouse clicks.  I found it very easy to have a content delivery system like Moodle and a phpbb3 forum set up and ready to go in a matter of hours.  I was anticipating it taking days or weeks.

Another task I have in mind is to port this blog over to the front page of algebrahut.com.  I think I read somewhere that could be done fairly easily.

As for other tasks, I have taken a break.  I seem to be at a dead-end for the 4-color theorem.  I thought I had something going, but when I finally sat down and tried to carry my ideas to their final conclusion, I wasn’t able to force only 4 colors upon my configurations.  I still had to accept that it might have been possible that a 5th color was needed.  It a sneaky problem.  Just when you think you’ve got it cornered, it gets away from you all the same.

The smart pen I’ve mentioned in my previous post continues to amaze me.  However, my students didn’t really seem to go for viewing the homework solutions with the audio.  It does take quite a bit more effort to do the homework solutions while having to explain them, and if they students continue to act disinterested in them, then I was stop doing the homework solutions with audio.  However, I can still use the pen for writing the solutions and uploading them without audio.  It will save me from having to scan one page at a time.

Well, I hope you’ll take the time to visit www.algebrahut.com from time to time.  I will be sure to post progress on this blog.

Thanks for reading.

~The Witchdoctor

In my previous post, I wrote about the Smart Pen from LiveScribe.  In a nutshell, you can write and record audio and the two are linked together.  This audio can be played back from the paper you wrote it on, uploaded to the computer for playback and searching, or shared online via LiveScribe’s website.  Sharing such a document online is called pencasting.

Here is my first decent pencast, on the topic of the Monty Hall Paradox.  Be sure your speakers are on and your flash player is up-to-date.

Please let me know what you think.  Thanks for reading.

~The Witch Doctor

Dear readers, I must beg forgiveness for not having written as much as promised lately.  I do not have a great excuse for it.  I just haven’t been in the mood to post anything great and I don’t want to post anything subpar.  I hope this post will pass the muster.

I wanted to share my excitement for this great new product I have only recently given a try.  It is called a Smart Pen, manufactured by LiveScribe.  It makes many great promises and, from what I can tell so far, it lives up to them.

Smart Pen

Finding a Safe Square:  Complex Elimination

Use of the Question Mark

 But consider the square right below this one.  It is also a 1.  What could that mean?

Using Info from a 2nd Square

Complex Elimination

 So, let’s reveal this safe square and see what we get:

Safe Square Revealed

This new information may not seem very useful.  There are 2 mines in the area of the square we just revealed, but there are still 6 unrevealed squares in the area.  One of them we know is a mine (marked with a flag), so there is one more mine in the 5 remaining squares.  How is that helpful?

We’ll have to use Complex Elimination again.  We will have to use the square next to it that is marked with a 3.  There are only 3 mines in the area of this square, two of which have already been located.  There is only one more, and it must be located in one of two possible squares:

Question Mark Again

Can you find the safe squares?

Complex Elimination Again

Here is my next move (again using complex elimination to find more safe squares):

Minesweeper

Next, I will write about how the same type of reasoning can be used to locate mines (and not just safe squares).  Thanks for reading.

~The Witch Doctor

This is a continuation of previous posts.

Finding a Safe Square: Simple Elimination

Now that we have found the location of some mines, we should try to determine if there are any safe squares we can reveal.  This is important not only because it is the game’s objective, but revealing a safe square reveals essential information to help us locate and mark more mines.

The easiest way to find safe squares is by Simple Elimination:  If an area only has 1 mine, and you have already located it, then all other squares in that area must be safe.  This happens for us in two instances:

Simple Elimination

The green box to the left tells us there is only 1 mine in the area, but we already have a mine marked in the area.  Thus, all other squares in the area must be safe.  I have marked them with an ‘x’.  Left-Click them to reveal them as safe squares and to get more information about other mines that might be close by.  It works in a similar fashion for the green box on the right as well.  Revealing all the safe squares marked with an ‘x’ yields:

Safe Squares Revealed

After revealing these safe squares, we will go back to mine-hunting mode.  With this new information, can we determine the location of any more mines?  You’ll find that this is the cycle of the game:  locate safe squares (and hence receive information), locate mines, locate safe squares, locate mines, etc.  

Can you determine the location of any more mines?  Here is the next mine I located (this was a No-Brainer minetype):

Result from Mine-Hunting Mode

Take note of the glowing square.  In my next move, I accidentally left-clicked it.  Accidentally revealing a square can happen easily, all the more so on a laptop.  Be careful not to accidentally click on the board.  It can instantly kill your game.  What happened to me?

Accidental Reveal

I got lucky this time, especially considering there are 4 mines in the area!  Yikes!  So I moved on to another part of the board.  Let’s go back to this area:

Remember from my previous posts, this one is not a No-Brainer.  But we can manage something here.  Read about it in my next post.  Thanks for reading.

~The Witch Doctor

This is a continuation of a previous post. 

Finding a Mine: The No-Brainer

The No-Brainer mine locations are the ones that require absolutely no thinking to deduce.  I had a few of these from the outset.  You know you have No-Brainer mines when the number on the square you are considering is the same as the number of unrevealed squares surrounding it.  Example:

No-Brainers

 I put a red circle and a green box around all the No-Brainer minetypes at this point in the game.  I will talk about two of them, labeled A and B in the picture above. 

For A, the number in the revealed square (within the red circle) is a 1.  This means that there is 1 mine in the surrounding 8 squares (located within the green box).  However, 7 of the 8 squares are already revealed and do not contain a mine.  This means that the last remaining unrevealed square within the green box must be the mine we are looking for.  Thus, we will mark it with a flag.

For B, the number in the revealed square is a 2.  This means that there are 2 mines in the surrounding 8 squares.  However, there are only 2 unrevealed squares where the mines could be.  Thus, these squares must be harboring mines.  There has to be 2 mines in the area, and these two squares are the only possible locations for them, so they must be the mines that are indicated by the revealed square 2.  Mark them with flags:

Mark the No-Brainers with a Flag

Counter-Example -  This is not a No-Brainer:

This is not a No-Brainer

The number in the red circle indicates there is 1 mine in the surrounding squares, but there are 2 squares still unrevealed.  That mine could be in either of the two unrevealed squares.  Thus, we cannot be sure where that mine is located.  Remember the first tip:  Do Not Guess.  Let’s see what else we can do with the board first.  Guessing is always a last resort and we haven’t tried anything else yet.  So, leave this alone for now.

Thanks for reading.  More to come.

~The Witch Doctor

This is a continuation of previous posts on MineSweeper.

The First Move

Start the game (and the timer) by picking (left-clicking) a square.  The first move is a crap shoot.  One of three things may happen:

• If you are unlucky, you will pick a mine and the game ends immediately. 
• A fair result is selecting a square that gives a number.  A high number (3,4,5) means you are in a hot zone with lots of mines surrounding you.  A low number (1,2) means it is relatively safe.  If you find a high number, you are better off picking another square on another part of the board.  If you find a low number, you can take your chances in that area or move to another area of the board.  It’s a toss up.  I think I would tend to stay put for the low numbers.
• If you are lucky, you will pick a square that is blank (no mine or no number).  This means you are in a safe zone with no mines surrounding you.  A bonus is that the game, instead of making you manually reveal all the surrounding squares which are guaranteed to be safe, reveals all the squares in the safe zone for you.

Here’s my first move:

Lucky First Move

This was a lucky first move.  A large part of the board is a safe zone.  You may consider this an advantage, but a big safe zone only means that there are big hot zones on other parts of the board.

 Thanks for reading.  More on MineSweeper is forthcoming!

~The Witch Doctor

I’m back from vacation. While on vacation, I picked up an old game I used to play:  MineSweeper!  I forgot how fun (and frustrating) MineSweeper is.  I thought that this would be a good blog topic.  I took several snapshots of my last game (see this post).  I will do my best to describe to you my secrets for winning this game consistently. 

Here is what the board looks like when you begin a game on Intermediate Level:

MineSweeper Starting Board

Objective

Find all the safe squares that do not contain a mine.  This implies that you must locate all unsafe squares that contain a mine.  For convenience, you are given flags to mark the unsafe squares.  The number of flags you are given indicates the number of mines on the board.

How To Play

To reveal a square, you must left-click it.  If it is an unsafe square that contains a mine, you blow up and the game is over.  If it is a safe square that does not contain a mine, you will be given some information:  the square will contain a number.  The number indicates how many mines are located in the 8 squares immediately surrounding the square you selected.  If no number is given in a square, it means there are no mines in the surrounding squares.  (See image and description of the first mine type below).

You are to use this information to determine the location of all the mines and find all the safe squares.  The only way you lose is by left-clicking on a square with a mine.

If you determine a square has a mine, you can mark it with a flag by right-clicking the square.  If you are uncertain about a square, you can also place a question mark on a square by double right-clicking the square.

Also, there is a timer on the game.  When you get good, it is fun to see how quickly you can find all the mines.  As a novice, I would just ignore the timer.  It will stop ticking at 999, but the game continues and you can still win.

In my next posts, I will talk about the logical thinking required to win this game.  But before I end this post, let me give you a couple of general tips on how to play (and win) MineSweeper:

Tip 1

Guess only as a last resort.

Many seem to think that choosing random squares at various points in the game is a good strategy.  I have found that other than the first one or two moves and sometimes the last one or two moves, guessing is rarely required

Tip 2

The rhythm of the game is usually as follows:  Locate safe squares, Locate mines, Locate safe squares, Locate mines….

Thanks for reading.

~The Witch Doctor

Here is a game of MineSweeper I played recently.  I didn’t take a picture of every single move, but it’s a fairly complete account of my game.  In coming posts, I plan to analyze some of the moves so that you too can win at MineSweeper.  I originally planned to make this one giant post, but it was getting too long, to the point that I was getting lost in writing it.  So, I am going to break this up into several posts.  What follows is the game I played, without commentary or analysis.

Lucky First Move

Safe Squares Revealed

Result from Mine-Hunting Mode

Accidental Reveal

Safe Square Revealed

Question Mark Again

Complex Elimination Again

Minesweeper

Minesweeper

Minesweeper