sudoku mania

I never pay much attention to the crossword-puzzle page of our regular newspaper DeMorgen. I did notice that they started a new sort of puzzle a few weeks ago but figured it had to be some bingo-like stupidity. It wasn’t until last friday that I had a look at the simple set of rules and I was immediately addicted (as I am mostly when the rules are simple enough!). One is given a 9×9 grid filled with numbers from 1 to 9. You have to fill in the full grid making sure that each number appears just once on each horizontal line, on each vertical line and in each of the indicated 3×3 subgrids!

It is amazing how quickly one learns the basic tricks to solve such sudokus. At first, one plays by the horizontal-vertical rule trying to find forbidden positions for certain numbers but rapidly one fails to make more progress. Then, it takes a while before you realize that the empty squares on a given line in a 3×3 subgrid cannot be filled with any of the numbers already present in the 3×3 subgrid. Easy enough, but it takes your sudoku-experience to the next level. Anther simple trick I found useful it to keep track how many times (from 0 to 9) you have already filled out a given number. If it is 9, you may as well forget about this number for elimination purposes and if it is 0 it will be hard to use it. Optimal numbers to use are those that are already 4 to 6 times on the board. And so on, and so on.

After having traced all back-copies of the newspaper I ran out of sudokus but fortunately there is a neverending (sic!) supply of them on the web. For example, try out the archive of Daily Sudoku, and there are plenty of similar sites as, no doubt, you’ll find by Googling.

An intruiging fact I learned from my newspaper is that there are exactly 6,670,903,752,021,072,936,960 different filled-out Sudoku grids. You then think : this should be easy enough to prove using some simple combi- and factorials until you give this number to Mathematica to factor it and find that it is

and hence has a pretty big unexplained prime factor! This fact needed clarification, so a little bit later I found this Sodoku players forum page and shortly afterwards an excellent (really excellent) Wikipedia on Sudoku. There is enough material on that page to keep you interested for a while (e.g. the fact that nxn sudoku is NP-complete).

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