Wednesday, August 22, 2007

Sudoku Lesson III - Virtual number pairs

Today's lesson is short and continues from Lesson II. As you are marking squares, you may find that the marked possibilities line up in a particular row or column. When that happens, you can project a "virtual" number across the row or up/down the column that the possibilities line up in:

As you can see in the above example, a virtual pair of 3's can be found in the bottom middle square, in boxes (5, 7) and (6, 7). Disjointed pairs of 2's and 5's in boxes (1, 7) and (2, 9) leads to the required virtual number pairs of 4's and 7's in boxes (3, 7) and (3, 8), because these are the only numbers left in the lower left square. Since a four from the lower middle square projects to the left, the solution to these boxes is easily recognized (and in fact, box (3,8) is improperly marked).

Sometimes projection of a virtual pair leads to a solution in another target square, and sometimes it uncovers another virtual pair. In the above example, an unmarked virtual pair of 7's can be solved in the top middle square, and that virtual pair leads to a virtual pair of 7's in the top left square, by projecting the virtual pair we marked in the lower left square. See if you can mark these virtual 7 pairs properly in the top middle and left squares.

Be sure to take advantage of this feature as you cycle through all nine numbers.

Monday, August 13, 2007

Sudoku Lesson II - Projecting the numbers

The easiest and most basic technique toward solving Sudoku puzzles is figuring out when a number must go in a box. One way to do this is to choose a number, then cycle thorough all the squares to see if the chosen number has been entered or not in the target square. If not, then project the number down rows and columns from other squares to exclude boxes in the target square. When all projections are made, if there is only one box where the number can go, write it in:

Here we can see that the number 1 fits in box (9, 9), then (8, 1,), then (3, 3).

If there are only two boxes in a square where a number can go, mark those boxes:

In this picture, the number 2 can go in boxes (1, 7) and (2, 9). If there are more than two boxes where a number can go, move on to the next target square and try again. Do not be tempted to mark three or more boxes. we need to save that kind of activity for later. Don't worry, I'll tell you when you can do that -- you gotta trust me for now.

Wednesday, August 08, 2007

42nd St. & 7th Ave. w/o Subway

These pictures don't do justice to the 80+ degrees and 100% humidity. Tea and Fresh, aren't u glad ur no longer here?

Monday, August 06, 2007

Sudoku Lesson I - Develop a Marking System

First, to avoid confusion, let's agree that a "box" is a space where numbers may be recorded and a "square" is a collection of nine boxes, 3 X 3, where the numbers 1-9 are recorded.

As you know, the puzzle comprises nine rows, nine columns and nine squares. The solution has the numbers 1-9 recorded in each row, column and square, with no number repeated. I admit that, when I'm solving a puzzle and I record two numbers the same in any row, column or square, I have borked it. When this happens, I find that it's extremely difficult to determine where I made a mistake. I usually just cross the whole puzzle off and move on. It's ok, you can do the same -- just chalk it up to experience.

The key toward solving any Sudoku puzzle is to have a good marking system. A marking system provides the solver with an indication of possible numbers that can fit in each box. In my system, I place a small dot in the box to indicate that a particular number should go in that box. The location of the dot inside the box determines which number it is.

I place the dot in the box in a 3 x 3 matrix fashion to represent 1-9, starting from top left for 1 and going to bottom right for 9. For example, in one of the boxes, i marked a "3":

For your convenience, I will identify particular boxes by a simple left-to-right, top-to-bottom coordinate system. In this picture, box (1,1) in the first square has a 3 marked in it.

Also in the above picture, box (3,3) has a 2 and a 7 marked in it. I will identify the boxes by column and row. So, for example, the 4 is in box (1, 3).

When recording dots, at first I never place more than two dots in any square, row or column. The reasoning for this will not become apparent to you until much later in the lessons, but if you remember this basic rule, it will make solving the puzzle much easier later on.

Saturday, August 04, 2007

Immigration Nation

I recently got an email with this comment:

Calling an illegal alien an undocumented worker is like calling a crack dealer an unlicensed pharmacist.

This nation was founded by people who were immigrants. Unless you are pure American Indian, your parents/grandparents/ancestors were immigrants. I highly doubt that illegal working aliens are putting a financial strain on this country greater than the value of the services they provide. If somebody can show me a study that determines their burden versus their benefit on the taxpayers of this great nation, then I'll listen more closely to comments like this one.

The measure of how great a country is can be determined by the number of people trying to get into it, minus the number trying to leave.