sudoku

It's a 9*9 matrix with 9 3*3 submatrices. Each submatrix must have 9 numbers from 1-9 with no repetitions. When one combines the 9 submatrices to get a 9*9 supermatrix, each row and column of the supermatrix must have 1, and only 1, instance of the numbers 1-9.
So one has 9 3*3 matrices, the numbers 1-9 inclusive with no repetitions for each 3*3 matrix. Then combine the 9 3*3 matrices so the supermatrix has numbers 1-9 in each row and each column without repetition..

So here's how you solve 'em.. 1) Go through each 3*3 submatrix, trying to find an obvious digit that fits, from 1-9.. Each time you find an obvious fit, one must go through the entire supermatrix of submatrices again, in the sequence 1-9. When you've exhausted the possibilities, it is time to guess.
2) Guess at one where a single digit must belong to one of 2 positions. Follow step 1, and if you run into an error, that guess was wrong, and the number must rest in the other position.
3) One can adopt another strategy.. For instance, if there are 4 digits possible for a space, say, 2,3,4,5... and in another submatrix space, there are only 2 possibilities, say, 2, 3.... then the probability of the 2 being in the space with only 2 choices is larger than the probability of the 2 being in the space with 4 choices...
4) Many times, the puzzle will be lacking in 1 or 2 numbers, with a lot of the other ones. This is meant to confuse you. Do not pay attention to the numbers which are missing and try to fill those in. Instead, when it comes time to guess, try to fill a row or column so that the row or column has lots of obvious fill-ins.
5) When you guess, keep track of the number of the guess, like, "OK, this is the first guess..." then, if you must "second-guess," and that guess is wrong, the first guess was wrong as well... this is why one guesses only when there there are only 2 possibilities...
6) I have guessed up to the 8th level, but, as I get better, it only takes me 3 or 4 levels... Ah, hell, just Google for a Sudoku solver !!! I'm sure a million have already been written !! Only takes a bit of linear algebra !! Thanks..

by Johnny Chingas January 31, 2007

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