Michael B Greenwald wrote:
Using only 2 simple rules it never had to backtrack (I guess backtracking would be equivalent to "guess-and-check"). To be perfectly clear, there were times (rare) when there was no square with a unique choice, but choosing randomly at that point never ended up getting me into a dead end.
Wow. How many times in a row can you flip Heads? Better yet, want to come pick lottery numbers for me? :-) Certainly you've just been getting lucky. The published puzzles are guaranteed to have only one solution, so every time you arbitrarily choose one of two possible values for a square, you should have a 50-50 chance of reaching an impossible position.
Rule 2 says that at any point, if there is only one square in a row, or a column, or a 3x3 box that contains some number n as a possible value (e.g. if a row has 4 open squares which could be, respectively (1,2,8 or 9), (1,8, or 9), (1 or 8) and (1 or 9), then the first square would take on the value "2").
Here's an example of a line of reasoning that you'll miss: add two more empty boxes to the above example, like so: {1,2,8,9}, {1,8,9}, {1,8}, {1,9}, {2,3,4}, {2,3,4} It's still the case that the first box must contain the 2, because the boxes {1,8,9}, {1,8}, {1,9} certainly account for all of the 1,8,9 among them in some order. There are extended discussions of computer solving techniques -- start at the giant user forum at sudoku.com and follow links from there, I think. --Michael Kleber -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.