Regruntled.com

Freaking News has some really strange pictures.  I think they got the idea from Jake Tucker on Family Guy.

An interesting idea: replace calculus with statistics.

From Saturday Morning Breakfast Cereal.

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.

With spectacularly bad timing, Farrah Fawcett dies on the same day as Michael Jackson.  Bam!  The media shift gears and Farrah is gone, forgotten.  The struggle with cancer is replaced by alleged pedophilia and drug abuse.

Bad Astronomy discusses the color illusion above.  The green and blue spirals are actually the same color!  I’ve overlaid a square of this color in the lower right to make this clear.