Started at 9, and now it's 1:30... please help...

Grifter730

Okay, I want to know what you think the next step is. I can't figure out any way to solve this. Please don't just spoil the whole thing by plotting in all the numbers. I won't learn anything that way. I just want to know what it is I should have spotted, what technique is used to solve it. For instance, you can say something like "r1c1 is 9 and r1c2 is 4 because of technique XY-wing". That way I can look up what the technique is, and how it's used to solve the puzzle. I'm just completely stumped right now and desperately in need of sleep.

bennys · Posted: Fri Sep 30, 2005 6:24 am Post subject:

angusj · Site Admin

angusj · Site Admin

Ruud · Site Admin

Before aiming the heavy forcing chain guns, just look at the candidates for digit 8.

Row 7 has 2 candidates in columns 1 and 4.
Row 8 has 2 candidates in columns 1 and 7.

Therefore digit 8 is locked in column 1, rows 7 and 8.

Eliminate digit 8 from r2c1, leaving r2c3 as the single candidate for row 2.

This completely breaks the puzzle open.

angusj · Site Admin

Ruud · Site Admin

You're right, AJ.

Didn't notice the candidate in r9c3. Embarassed

By coincidence, it did lead to the solution.

Grifter730 · Posted: Fri Sep 30, 2005 2:10 pm Post subject:

Okay, so I used the method given in the first response (something called the Uniqueness test), and it worked perfectly, it's awesome. I'm wondering though, in the link given, it seems as if this method only works when a puzzle is "unique" and has only 1 solution. So, does ALL puzzle only have 1 solution...?

Lummox JR · Posted: Fri Sep 30, 2005 7:18 pm Post subject:

All valid sudoku puzzles have one solution, yes. Otherwise, you'd be absolutely forced to abandon logic at some point to solve the puzzle.

The uniqueness test is quite fascinating, really. It doesn't prove the puzzle is unique, but relies on the conditions of sudoku which say it is. No test, really, can prove a puzzle is unique except a lot of T&E and backtracking, which is essentially as good as throwing it into a dancing links solver. Any generator worth its salt (or any hand-setter worth theirs) should be testing created puzzles for such a problem. After all, since uniqueness is one of the initial conditions, a multiple-solution board is just as wrong as one with two 5's in the same box.

Interestingly someone has just discovered a fourth variant of the uniqueness test, which before this was only known to exist in three flavors. I've been searching for a bit to see if I could find a puzzle that relies on the new technique.