Regruntled.com

Here are 2 superposed puzzles.  You can solve one puzzle with the digits, using a pencil, and then solve the other puzzle as a color sudoku, using colored markers.  Each puzzle has a unique solution, but the two solutions are different, since the digits and colors don’t match consistently (look at the 3s and 9s).

Alternatively, you could try to solve both puzzles at the same time.  It seems that the 6s are always light blue, and are easy enough to finish off. 

Reading about the many-worlds interpretation of quantum physics seems to have warped my tender little mind.  In the spirit of quantum superposition, the digits are arranged in one sudoku pattern, while the colors of the digits are arranged in a different sudoku pattern.

Here is a YouTube video by P. Stacey that uses an interesting representation of sudokus. The grid is gone, and the cells are now round dots. No corners, and lots of white space! Different colored dots have different sizes, which adds a sort of visual texture, as well as softening the regularity of the 9-by-9 array.

There is a famous chess puzzle that calls for placing 8 queens on a chessboard such that no two queens can attack each other.  In other words, no two queens can be on the same row, column or diagonal.  This puzzle is of some historical interest in that it caught the attention of mathematicians like Gauss and Cantor, but nowadays it is easy enough to solve by computer that it is given as a homework problem in programming courses.

A sudoku is 9-by-9 instead of 8-by-8 like a chessboard, but the restriction on rows and columns is similar. A sudoku doesn’t have any restrictions on diagonals, but it does have the restriction on 3-by-3 blocks.  What happens if we add the sudoku block restriction to the 9 queens problem?  The 9 queens problem is known to have 352 solutions, and it turns out that 144 of them satisfy the sudoku restriction.

The next question is whether 9 of these 9-queens patterns can be combined into a sudoku.  The answer is no.  There is just no way to do it without the patterns interfering with each other.

I’m not sure whether this is aimed at people who like sudoku, or people who don’t like sudoku.

I’ve been experimenting with metrics for sudokus.  For example, in the image above, each color occurs once as the center of a 3-by-3 block, four times as a corner, and four times as a side. There are also no instances of squares of the same color being adjacent diagonally, which is allowed by the sudoku rules is the squares are in different 3-by-3 blocks, but which visually makes the distribution of that color seem less random.

My thinking is that images with certain properties are more esthetically pleasing than other images.  I have a computer program that generates sudokus, and I can plug in different metrics.  The metrics also restrict the number of sudokus generated to more manageable levels.  The image above is one of only 36, for example.  Runs with less restrictive metrics go into the tens of millions.

For a while now, I’ve been thinking about making some kind of reconfigurable medium scale color sudoku. There are a number of possibilities: Post-its, construction paper and sticky spray, flannel boards, velcro, pegboard, etc.  And refrigerator magnets. It turns out that craft stores sell sheets of magnet with a peel-and-stick adhesive on one side, making it possible to turn just about any small object into a refrigerator magnet. I found some 2-millimeter foam sheets in a variety of colors, cut them into 2-inch squares, and attached magnets.  The resulting sudoku is about 18 inches on a side.

Ideally, the magnetized objects should be rigid, like ceramic tiles or plastic squares.  The foam had the advantage of coming in 9 different colors, no painting required.  Cardstock was another option, but I thought the foam would be less likely to be damaged by water.  It’s an experiment.

“Well, how did I get here?”

I’ll tell you how I got here:

“One thing led to another.”

I had a few thousand sudokus in a database, and I wondered if I had any duplicates or near-duplicates.  I had the computer compare each one to all the others (we’re up into the tens of millions of comparisons), and found a number of pairs that had 6 colors the same and 3 colors different.  I was looking back and forth trying to compare them.  I didn’t have blink comparator handy, but I realized that if I put them in Windows Movie Maker, the “dissolve” effect would highlight the differences.  This looked interesting; was there a way to find a sequence of sudokus, each one with 3 colors different from the previous sudoku?  This turns out to be a “six degrees of separation” type of problem, easily solvable by computer.  And that’s how I got here.

From the Sydney Morning Herald:

AFTER 105 witnesses and three months of evidence, a drug trial costing $1 million was aborted yesterday when it emerged that jurors had been playing Sudoku since the trial’s second week.

In the District Court in Sydney, Judge Peter Zahra discharged the jury after hearing evidence from two accused men, one of their solicitors and the jury forewoman, who admitted that she and four other jurors had been diverting themselves in the jury box by playing the popular numbers game.

Will sudokuholism be the latest excuse to avoid jury duty?