... by: Vijay, Michigan

Load Sudoku: 296857431741932865583641927408513092100294008902786004320168049619475283804329006

I discovered a uniqueness strategy that is not currently in the solver, and you may want to code it. In this sudoku:

D2,E2,E3,F2 have candidates 67,36,35 whereas
D7,E7,E8,F7 have candidates 67,36,57,135

Looking at the two columns we can conclude, F7 must be 1, otherwise the sudoku will lose its uniqueness.

Once again, great site!
Andrew Stuart writes (10-Sep-2009):
I'm coded your strategy and I'm afraid it fails. :(

I have a counterexample here

...9...86......5......5...13261.9.547185..6934..36..1.2....3.6..4.69..7.67..1.4..

G3 = 1/9
G7 = 1/8/9 <-- should be able to set to 8
H3 = 1/3
H7 = 1/3

And 8 is the wrong answer for that cell. The reason you have gone astray is that unique rectangle are built from four cells with potentially the same pair. Your strategy calls for two different pairs in a rectangle + one other candidate, and you are implying that that extra candidate must always be the answer. In your example it is true. And I have found several examples where it does work - but only accidentally. 1/9 + 1/9 + 1/3 + 1/3 (in my example) does not imply a violation of uniqueness. Each set of two pairs will be determined by candidates elsewhere on the board.

Good try though.

... by: J, US

In your naked triples section you list possible triples as the following:

123, 123, 123
123, 123, 12
123, 12, 23
12, 23, 13

Would the following also be triples or not:

123, 12, 13
123, 13, 23
123, 123, 23
123, 123, 13

If they are not, what is the reasoning behind it? Following the logic from the first four, it seems these last four would also be triples???

Thanks!
Andrew Stuart writes (10-Sep-2009):
Yes, all those are valid triples. I didn't set out an exhaustive list

... by: APPLECORE, USA

You may have answered this directly or by inference but: Is every Suduko puzzle solvable by rules of logic, without relying on trial and error? Or are some puzzles only solvable by trying a possible solution?
Andrew Stuart writes (10-Sep-2009):
Every puzzle *ought* to be solvable by logic - it is after all a confined finite puzzle. But it has great depth and I do not know how to solve every puzzle with the strategies I have. Others may have more but I don't know of a general theory or a universal solver yet, other than brute force. People also split hairs over what constitutes logical as well, so the area is murky. Currently if I produce a set of puzzles at random and then grade them, about 0.2% will be unsolvable by my methods.

... by: Rick Cromer, Texas, USA

Load Sudoku: 000470930003200006070090281408020600765080342001030708146050090200007100087069000

Here's another contender for the easiest Sudoku puzzle
Andrew Stuart writes (31-Aug-2009):
To many clues I'm afraid (39). There has to be a maximum otherwise a sudoku with one number missing could be the "easiest". So partally finished puzzles are going to grade easier than full ones. Etc

Maximum clues are 32

... by: walt r, usa

kenduko27 doesn't seem to get the right answer and it rejects the correct answer???
Andrew Stuart writes (27-Aug-2009):
I found a javascript bug which was preventing the solver from continuing (KenDoku only). I've fixed it and it should be going OK now

... by: Dick, USA

Load Sudoku: 238479500567218943419356827840923700370064298920087430654732189182695374793841652

Problem solver indicated Unique 5 at D9 would lead to solution. I maintain this is an unsolvable puzzle since a "1 at D9" would also lead to a solution.


Andrew Stuart writes (8-Aug-2009):
Dick, please click Solution Count, which finds 5 solutions. The solver is for sudokus with a unique solution. Specifically, the Unique Rectangles strategy, used by the solver, is not valid for sudokus which have multiple solutions. When given a sudoku with multiple solutions, the solver may be unable to find any solution or it may find one of the valid solutions.

... by: Rob Miller, none

Load Sudoku: none

Cool site.

... by: Geoffrey Howell, Australia

Load Sudoku: 000081000600000030004000000020000805700400000000000100000650040309000000080000000

Dear Andrew,

I found this puzzle that your systems says cannot be solved yet has one solution. I believe you're interested in such examples.

Geoffrey

PS I use a compacted form to hold my Sudoku puzzles: A is one zero, B is two zeroes etc. It takes about half the space.
Andrew Stuart writes (7-Aug-2009):
The message "Run out of known strategies" is valid. Not all sudokus with unique solutions can be solved with the known strategies. As new strategies are developed and adopted by the sudoku community, I plan to implement them in the solver, as I have done in the past.

... by: Gene, California

While solving a puzzle, one of your steps refers to "SINGLES CHAIN (Type 1)"
I can't find a description of this logic on your web page.
Can you help?
Thanks, Gene Tissot

Andrew Stuart writes (17-Aug-2009):
http://www.sudokuwiki.org/Singles_Chains

... by: Marcel Cox, Luxembourg

Load Sudoku: 100000000000900006805000700040000900000805000000010030000000010000000450020700000

Is there any chance of getting the grader back? I would like to compare the difficulty of the Sudoku mentioned in this post with a few others. The author of this Sudoku thinks he has beaten the most difficult Sudoku in the world,but I don't agree with him. His Sudoku is just very hard for brute force attacks because of the few hints it has. However resolving it by deduction only requires one difficult step among otherwise simple steps.
Andrew Stuart writes (2-Jul-2009):
This has quite a low score but is just a diabolical

17 clue sudokus are usually quite hard for brute force but they exist across the whole spectrum of grades.

... by: KM, US

I noticed in your new killer solver that the solver doesn't check the individual sums of the cages early on. For example, a cage of 2 blocks that needs to add up to 11, where one block has been narrowed down to 7 or 8, and the other to 7, 8 or 3, is essentially already solved, but the solver doesn't catch onto this until much later through some more complex strategies. Also, I had one where a cage of 2 blocks needed to add up to 7, and the one block was a 4. The second block should have been solved, but the solver didn't catch onto this until much later.

The solver definitely does the trick, but doesn't necessarily always take advantage of what I would consider already solved squares.

I've been solving killers by hand using the edit option in your regular sudoku solver for nearly a year (I'm too lazy to actually use a pencil and paper), but this definitely makes it easier since I don't need a second window open with the actual layout of the killer that I'm trying to solve. :-) Thanks!
Andrew Stuart writes (2-Jul-2009):
I think that was a bug. I've loaded a new version now. You might have to clear cache (I hope now). I'd be very interested to know if the problem has cleared up. I realised there was a problem myself when the tough example didn't solve.

Bug reports like this most appreciated

KenKen 6x6 is in trial at the moment, hope to release soon :)