SuDoku question

Originally posted by geepamoogle
I am just curious if anyone knows whether or not bifurcation or the "brute force" method is sometimes absolutely necessary to solve one of the tougher Sudoku

For those of you who don't know bifurcation refers to when you try out each possibility for a locatio for which it could be a limited number of options (usually only 2), and then eliminate the on ...[text shortened]...

Any other super-advanced techniques or logic which could proceed forward from this point?

Yes .. After this only brute force bifurcation will work. Nothing else.

Originally posted by geepamoogle
I am just curious if anyone knows whether or not bifurcation or the "brute force" method is sometimes absolutely necessary to solve one of the tougher Sudoku

For those of you who don't know bifurcation refers to when you try out each possibility for a locatio for which it could be a limited number of options (usually only 2), and then eliminate the on ...[text shortened]...

Any other super-advanced techniques or logic which could proceed forward from this point?

Each row and column adds up to 45...agreed?

each soduko is 9 lines across, 9 lines down for a total of 810..agreed?

So...divide the soduko in half vertically and then horizontally and then diagonally. What you will find is areas of the puzzle that have low values and those that have high values.

It's pretty easy from this information to then determine whether an 8 or a 2 goes in a given box.

Originally posted by geepamoogle
I am just curious if anyone knows whether or not bifurcation or the "brute force" method is sometimes absolutely necessary to solve one of the tougher Sudoku

For those of you who don't know bifurcation refers to when you try out each possibility for a locatio for which it could be a limited number of options (usually only 2), and then eliminate the on ...[text shortened]...

Any other super-advanced techniques or logic which could proceed forward from this point?

the idea behind a sudoku is that it can be solved without guessing. If you have to guess, its not a sudoku

Originally posted by clandarkfire
the idea behind a sudoku is that it can be solved without guessing. If you have to guess, its not a sudoku

xxx xxx xxx || xxx xxx xxx || xxx xxx xxx
xxx xxx xxx || xxx xxx xxx || xxx xxx xxx
xxx xxx xxx || xxx (AB)(AB) || xxx xxx xxx
================================
xxx xxx xxx || xxx xxx xxx || xxx xxx xxx
xxx xxx xxx || xxx xxx xxx || xxx xxx xxx
xxx xxx xxx || xxx xxx xxx || xxx xxx xxx
================================
xxx xxx xxx || xxx (AB)ABC || xxx xxx xxx
xxx xxx xxx || xxx xxx xxx || xxx xxx xxx
xxx xxx xxx || xxx xxx ABC || xxx xxx xxx


The uniqueness technique is as follows. (X's mark unimportant locations)

If R7C8 was not "C", then we'd be left with 2 rows, 2 columns, and 2 boxes where one pair is A, and the other pair B, but you could swap them and arrive at another solution which also works just as well. Because we assume the sudoku is legitimate, and therefore has one solution only, it has to have C in R7C8.

I've found thus far that this serves as a shortcut, but have yet to see a situation where it has to be used.

Originally posted by uzless
Each row and column adds up to 45...agreed?

each soduko is 9 lines across, 9 lines down for a total of 810..agreed?

So...divide the soduko in half vertically and then horizontally and then diagonally. What you will find is areas of the puzzle that have low values and those that have high values.

It's pretty easy from this information to then determine whether an 8 or a 2 goes in a given box.

I don't see where you get a total of 810

9 columns * 45 = 405
9 rows * 45 = 405

the rows and columns overlap; you shouldn't count them twice

Originally posted by forkedknight
I don't see where you get a total of 810

9 columns * 45 = 405
9 rows * 45 = 405

the rows and columns overlap; you shouldn't count them twice

405 across + 405 down = 810

For the most part you only use the 405 but the 810 can be helpful when looking at whether your columns or rows need higher lower numbers.

Honestly, I never found sums useful for Sudokus..

They are much more of a logic-based problem with a minimum of actual mathematics.

You could replace them numbers with letters or symbols without changing the nature of the puzzle, which isn't the case with some other puzzles like Kakuro (where the sum of the digits is noted for each row and column).