Absent For A Bit ....

I am away for a little while working on a few or more episodes for The Adventures of My Space Alien Alter Ego story ... will return (to Earth) soon!

Notice: Blogger has screwed up and lost a bunch of photos out of my blog! They are replaced with a gray silhouette of a human head. I will eventually get them replaced with the correct photo, it may take a while to find and fix everything. So some of my stories don't make much sense without their photos, sorry for the inconvenience.



Sudoku Rectangular A-B-B-A B-A-A-B Rule

While playing Sudoku this morning I think I noticed something new (at least for me).

Every Sudoku puzzle is supposed to have a unique solution. It is not supposed to be possible to have a pair of numbers in a 3x3 square that can be switched and then have the corresponding pair in another 3x3 square to the side or above or below then just be switched, what I call an A-B, B-A -> B-A, A-B swap AND have those 4 cells form the corners of a rectangle
(see fig 4).

For instance, this morning in a puzzle I had deduced that the pair of numbers at pair position A-B was 1 and 6, (see fig 1) but didn't know which order. Shortly after that I figured out that B and A' were also 1 and 6, (see fig 2) in the middle column of the puzzle, but again I didn't have enough information at that time to make a final determination of the pair B and A'. Then I tried to figure out the position labeled ? in fig 3. At that point I realized that the cell at B' could not contain a 1 or 6.

Reason: If A & B and B' & A' can be swapped with 1 and 6 or 6 and 1, then there would not be a unique solution to the entire puzzle. The swapping of 1-6 & 6-1 to 6-1 & 1-6 would not break an otherwise completed Sudoku puzzle, as each row, column, and 3x3 grid would still contain 1 through 9

Fig 1

Fig 2

Fig 3

Fig 4 Illegal Combination

If my logic is incorrect, incomplete or unsound, please let me know.

This may prove to be a useful tool when trying to solve a Sudoku puzzle. I don't think I have seen this "trick" explained before.

Update 2009.04.08 - Note: All 4 corners of the rectangle have to be updateable cells for this rule to apply. Sudoku games begin with a certain amount of cells filled in, non-updateable. I noticed several examples in completed puzzles where rectangles do exist, but at least one of the corners was a non-updateable cell, to which this rule does not apply, hence the alternating A-B-B-A B-A-A-B in the title.

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New Blog for My Abstract Art ... Come Visit

Click HERE for the Art of Ernest S B Boston

These are pieces that I have generated mainly using computer art tools. Enjoy !

Something New:

I am also in the process of linking my poetry blog entries together. This project is only partially finished. A "Poetry LINK" at the bottom of the blog entry points to the next older piece of poetry.

First poem in the series of linked poems ....

Turn Gold Out of the Darkness

Turn Gold Out of the Darkness

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My Art

These are some of my abstract art pieces. They are available as prints, send me a note if you are interested.

Couch Glow

Couch Glow

Gold As Smoke

Gold As Smoke

Flowing Wood

Flowing Wood