> otherwise, there is an > obvious "mathematically guaranteed way of solving the puzzles" > in principle. Is there not?
Yes, there is. Let P be a Sudoku puzzle specified as a 9 9 matrix with the blank squares being 0. Then u=: 1+9 9$"1 (#:i.@(*/)) 9^81x generates all possible 9 9 matrices of the integers from 1 to 9; u=: (#~ ((0=P)+.P&=)"2) u selects matrices that have the specified digits in P in the correct places; u=: (#~ f ) u selects the matrices with all 9 digits in each row, where f=: (9$1) -:"1 */@((1+i.9)&e.)"1 and u=: (#~ f@:(|:"2)) u selects the matrices with all 9 digits in each column, and u=: (#~ f@:(,/@((;~9$1 0 0)&(,;.1))"2)) u are all the solutions for P. ----- Original Message ----- From: Jose Mario Quintana <[email protected]> Date: Tuesday, March 17, 2009 11:52 Subject: [Jgeneral] [JGeneral] The first mathematically guaranteed way of solving Sudoku puzzles? To: [email protected] > Yesterday I read an article in USA TODAY about "the first > mathematically guaranteed way of solving the puzzles;" see > http://www.usatoday.com/tech/science/mathscience/2009-03-15- > sudoku-secret_N.htm. It reminded me of an interesting old forum > thread: http://www.jsoftware.com/pipermail/programming/2005-December/thread.html#298 (see > also http://www.vector.org.uk/archive/v214/sudoku.htm) and a hint from > an academic female adviser "It is not just about laying the eggs; you must > know how to cluck them." > > In any case, it seems to me that the 'way' should be qualified, > in some sense, as 'implementable;' otherwise, there is an > obvious "mathematically guaranteed way of solving the puzzles" > in principle. Is there not? ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
