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- nanaosei_2007
**Posts:**1**Joined:**14 May 2015

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

- denis_berthier
- 2010 Supporter
**Posts:**1261**Joined:**19 June 2007**Location:**Paris

2 posts
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