Dear Joshua & Mike: I see now what you're saying. No, I implemented a strictly weaker rule, but your rule is more elegantly stated. I'll run some tests. If it can solve "Diabolical" level Sudoku's, then it would be too strong. The intuition of your rule is that if one square isn't strong enough on its own (singleton set) to lay down suppressing fire & kill off pretenders to the digit, then groups of squares might be able to suppress some pretenders. At 08:51 AM 6/30/2006, Joshua Zucker wrote:

I'm not clear from your description of level 1 whether you look at every set of k cells -- if a set of k cells out of 9 includes at most k different digits, then those k digits can't appear anywhere else in the set of 9. (I was very pleased when I realized that this rule with k = 1 and k = 8 covered the two usual simplest rules, "if a cell can contain only one digit..." and "if a digit can appear in only one cell...")

--Joshua Zucker