MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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:




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?

share|cite|improve this question
Isn't there already a general framework for Sudoku-like problems?: – Sam Hopkins Jun 14 '13 at 16:06
Matroids can help with Sudoku verification. See and… – 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?): – Timothy Chow Jun 14 '13 at 20:54

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.