Regruntled.com

Another experiment.

Here’s the result of a typo in one of my programs.  I left out a “-1″.  I’ll take creativity where I can find it.

 

A Voronoi sudoku with each cell outlined in black.  It turns out that the outline can be added later with Paint.net.

I was reading about Voronoi diagrams (is that a cool name or what?) and I decided to adapt one of my sudoku programs to generate them.  Each cell in the sudoku gets a central point, somewhat off the grid, and each pixel in the image is colored the same as the nearest central point.  This leads to a mess of squarish-but-irregular shapes that somehow fit together.

From Swedish hacker Hans Anderson, who also built Tilted Twister, the Rubik’s cube solving robot.  I’d like to point out that what the robot finds easy, namely solving the sudoku, is difficult for humans, while what the robot finds difficult, namely reading the numbers, people find easy.

When mathematicians count the 5,472,730,538 possible sudokus, they count the diagrams above as one sudoku, not two.  The sudokus are said to be isomorphic because one can be transformed into the other by rearranging the rows and columns and relabeling the digits without disturbing the essential “sudoku property” that every row, column and block consists of 1 through 9.  Since the sudoku property doesn’t change, it’s still the “same”  sudoku pattern.

Well, this makes sense in an abstract, mathematical way, but what does it feel like to the person solving the sudoku?  I decided to find out.  I printed out the two puzzles and solved them.  There are some similarities that relate to the way I solve puzzles.  For example, both diagrams have two columns with 5 cells filled in, and there are often opportunities to complete such columns.  Both diagrams have one row with a single element, and I tend to avoid such rows. 

I knew that the sudokus were isomorphic, so it was easy to pick up on a few similarities.  Even so, solving one didn’t make it any easier to solve the other, and if I hadn’t set up the isomorphism myself, I never would have suspected.

It’s tempting to conclude that the human sudoku solver does not solve the underlying abstract sudoku, he solves the particular representation in front of him.  This is not quite right, because I think I would notice something simple, for example if the two diagrams were identical except for the 6s and 9s being switched around. 

On the other hand, now when I find a particularly good source of puzzles (like the “evil”  Times of Malta sudoku on Sundays), I can run them through my rearranger and make several puzzles out of each one.

Conceptis has a series of pictures of sudoku-themed quilts.  This particular quilt has an error in it.  I suppose the artist could be challenging the viewer to question his assumptions about sudoku-ness… or it could be a stupid mistake.

See also:

• Patchwork sudoku
• Sudoku quilt

It’s not a waste of time, it’s an obsession!  That’s different.  Note that it’s a rainy day.  What’s Grandpa supposed to do, take Ruthie for a walk in the rain?

I’m trying out PictureTrail.com, which will do some cool animations on uploaded pictures. Of course, the next step would be to find 6 color sudokus that will line up along the edges.  I suspect that the easiest way to do that would be first to find a way to color the edges that satisfies the sudoku constraints on all 6 sides.  That sounds easy enough to do manually.  Then I could have my computer fill in the sides, and I already have a program that could be modified to do that.  The tacit assumption is that for any valid border (4 sides, 32 cells), there is a way to fill in the interior (49 cells).  I don’t know for a fact that that is true, but I suspect that it is.