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 _sudoku_s. 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

$2^{20} \\times

3^{8} \\times 5 \\times 7 \\times 27704267971$

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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