Solving Sudoku using linear algebra's Simultaneous equation

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Solving Sudoku using linear algebra's Simultaneous equation

Postby nanaosei_2007 » Thu May 14, 2015 9:00 pm

goto this page to read more.

http://mprodcers.blogspot.com/
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Re: Solving Sudoku using linear algebra's Simultaneous equat

Postby denis_berthier » Fri May 15, 2015 3:52 am

nanaosei_2007 wrote:goto this page to read more.

http://mprodcers.blogspot.com/


Hi nanosei_2007,

The idea of using linear equations is an old and obvious one. You show a particular example for which it works.
However, it has never worked in general for a very simple reason:

In standard (i.e. 9x9) Sudoku, you have:
- 9x3 = 27 linear equations (9 rows, 9 blocks, 9 columns)
- 81 - #givens unknowns, which is in general much more than 27
so that the obvious linear system is largely under-constrained.

You must add:
- constraints 1 ≤ x ≤ 9 for all the unknowns
- constraints about uniqueness in each unit
which together take you far from mere linear algebra
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