That's a perfectly good deduction, but you've stated it wrong. If the 2 Z's in the first row can only be 2 and 6, and similarly for the last row, than no other number in either row can be 2 or 6. The same holds for the two columns. It even has a name, but I'm not certain what it is. Perhaps "X-wing". -- Stan Isaacs
Sudoku: I ran across a moral dilemma in a Sudoku last night: Can I use the uniqueness of the solution to exclude some lines of argument? My partial solution looked like this:
Z - Z | * * * | * * * x - x | * * * | * * * x - x | * * * | * * * --------------------- x - x | * * * | * * * x x ? | * * * | * * * x - x | * * * | * * * --------------------- x x x | * * * | * * * x x x | * * * | * * * Z x Z | * * * | * * *
x is a known value, - is an empty cell (so far), * could be either.
I knew that the left column Z,Z values had to be 2,6 in some order, and the third column Z,?,Z values had to be 2,3,6 in some order. I observed that, if I assigned 3 to the ?, that the Zs could be either 2,6 and 6,2, or vice versa. If one solution worked, the other would also, since all the puzzle constraints on uniqueness etc. would be satisfied in either case. Hence, if I used my meta-knowledge of a unique solution, I could exclude the value 3 in the ? cell. Dilemma: Is this fair? In a race, there's no way to exclude the inference; and we used to do similar things on multiple choice tests. But for self solving, should the conclusion be allowed?
Rich
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-- Stan Isaacs 210 East Meadow Drive Palo Alto, CA 94306 stan@isaacs.com