Here is a Sudoku 'almost' finished that still needs a 'guess' (I think)
+-------+-------+-------+ | 3 6 7 | . 4 . | 5 9 2 | | 9 5 2 | 3 7 6 | 4 1 8 | | 8 1 4 | 2 5 9 | 6 3 7 | +-------+-------+-------+ | . d 8 | 6 2 c | 7 5 . | | 5 . 6 | 4 9 . | 2 8 1 | | . 2 b | a 8 5 | 3 6 . | +-------+-------+-------+ | 6 4 3 | 9 1 2 | 8 7 5 | | . . . | . 3 4 | 9 2 6 | | 2 . . | . 6 . | 1 4 3 | +-------+-------+-------+
Can you complete without a guess to eliminate an option?
this can be done with the technique described as "forcing chains" by michael kleber in a message a few months back. i've labeled the relevant squares above. square (a) is either 1 or 7. if square (a) is 1, then square (b) is 9. if square (a) if 7, then square (c) is 1, and then square (d) is 3, so again square (b) must be 9. thus in either case, square (b) must be 9. the rest can easily be filled in from here. mike