Did it, like a Medium, whatever they are. (I forget)
Difficulty score 30. No green.
I may have solved that by an illegitimate technique. I'll have to think about what I did and see if I can justify it.
Suppose you can prove cell A cannot be x implies cell B cannot be y and you can prove when cell B is not y cell A must be x. Does that mean cell A must be x?
Suppose that you prove that when cell A cannot be x implies cell B cannot be y and when cell B is not y cell A must be x but in either case cell C must be z. Does that mean that cell C is z?
I used the "technique" of assuming cell C must be z and it worked. But that may have been just a fortunate coincidence and not correct logic.
I think I am correct because I have covered all cases. Either cell A is x or it isn't but in either case cell C must be z.
However, I may not have covered all cases when cell A is x!
I may have only covered 1 special case where cell A must be x.
That is why it would really be good to answer my first question. In which case the real technique is that I have proven cell A must be x.
Here is the logic in simplest terms. If A implies B but B implies not A then is A true or false? Or is it not possible to say?
I think this is proof (or disproof by contradiction), so A is not true.
If so, then my new techniques are correct!
Actually this is not a new technique, just a n
...just a new wrinkle on an old technique of following an alternating inference chain until it proves impossible to solve the puzzle with the original assumption. At that point you have proven the original assumption false and can fill in the first cell in the chain with the digit you assumed did not go in that cell.
A little more thought and I am convinced that the 2nd technique (the one I actually used) is not correct! So I solved this one with a "lucky" guess.
Oh Bleep! Just read all that and I think my head exploded. Gee thanks, 'drwho'...
Done with greens
To headless Lin, sorry about that.
The short explanation of where I went wrong is this: If A implies B that does not prove that B implies A. But that is the wrong assumption I used.
In Iron Sudoku getting the right answer is all that counts. In philosophy and math correct methods are at least as important as correct answers.
go - for real this time
made a quick trip to Tennessee, for a funeral... 4 days to catch up on. I might not make them all tonight, but regardless... go!
I just don't have it in me to finish the two experts... goodnight sudokuland!