Sudoku.com has a new tutorial on solving Sudoku grids. This little “how-to” is nice in that it follows along in solving an actual medium difficulty puzzle, offering the reader the ability to mouseover the diagrams in order to see each part of the solution as it is described.

Sudoku puzzles: how to solve

(via Lifehacker)

Sudoku’s been a bit of an obsession of mine for a while, although that initial, heady, infatuation has faded a bit. I still find it a great way to occupy my mind and keep my logic muscles toned.

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Another great way to keep your mind in tune is workout your body. I found that my mind is more sharp & focused if I workout and have a healthy meal each morning.

Yeah, but that involves, like, exercise. Sweaty stuff is anathema to me, for the most part.

Of course, you can do Sudoku on the train. My fellow commuters probably wouldn’t appreciate me doing calisthenics.

That said, I have been trying to get out running lately.

Interesting game. I think someone once left a printed copy filled out in the bathroom stall.

Want an exercise for the mind. Write some code to solve Sudoku. The grid is a simple two dimensional array.

Now that I think about it, here is a better exercise. Try to find out how many possible board exist.

A lot of the mathematics of Sudoku is available in the Wikipedia article.

http://en.wikipedia.org/wiki/Sudoku

There’s 6,670,903,752,021,072,936,960 possible grids.

I read that Wikipedia article. Then I did some simple math and determined that the number seemed really off. I even took the easy approach and calulated a Latin square of the same size and came up with a much smaller number. A Sudoku is just a subset of a Latin square. It does not have the restriction in the smaller squares.

Start in the upper left corner of an empty grid and ask the question, “how many different symbols can be placed here?” Nine is the obvious answer. Next cell to the right, Any of the eight remaining. This continues down to one. That would be 9! for the first row.

Next row. First cell. It can be anything except what is in the cell above it. Eight options. Next cell to the right can be anything not above or to the left. Seven. This continues.

In the end you get (9!) * (8!) * (7!) * (6!) * (5!) * (4!) * (3!) * (2!) * (1!) which equals 1.83493347 × 10^21. This is around one fifth of the number they get. I realize the difference. My calculations does not take into account the different patterns that are really all the same game. For example, if you swapped all the twos with all the nines, you get the same game with a different representation. (Maybe you could write an online version that uses pictures of your nine favorite brews) For this you would have to multiply my result by 9! (362,880). The Wikipedia article links to the source for that number and they explained the same situation. Although I also found mention of the “known” Latin square permutations and it is way off from my number.

I’m not even getting into the games that are the same when you rotate or mirror the grid further reducing the number.

I can either exercise my mind more or go on with my life.