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Advanced sudoku-solving seems rather streamlined:

  • for each square write down the acceptable values
  • Using a standard set of techniques - many of which I did not know by name - deduce the values of certain squares or rule out possibilities.

There seem to be a few more techniques with interesting names:

x-wing

swordfish

xy-wing

unique rectangle

Can matroid theory offer a general framework for these techniques?

What happens when you try to solve the "generalized" sudoku's you see in magazines? I try to imagine the numbers 1..9 like basis vectors in some crazy vector-space-like object and we need to check these "independence" conditions as we look from various angles. Can this be formalized?

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1  
Isn't there already a general framework for Sudoku-like problems?: en.wikipedia.org/wiki/Exact_cover – Sam Hopkins Jun 14 '13 at 16:06
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Matroids can help with Sudoku verification. See mathoverflow.net/questions/129600/is-there-a-sudoku-matroid and mathoverflow.net/questions/129143/… – Tony Huynh Jun 14 '13 at 16:42
    
It will be worth my time to study Knuth's "dancing links" algorithm! – john mangual Jun 14 '13 at 18:22
    
A very closely related MO question (a duplicate perhaps?): mathoverflow.net/questions/129600/is-there-a-sudoku-matroid – Timothy Chow Jun 14 '13 at 20:54

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