The New Sudoku Players' Forum

[fizx1]

There are at least 3 solutions to this puzzle, and that is why you have to use trial and error.

[simes]

There are at least 3 solutions to this puzzle, and that is why you have to use trial and error.

I think it has a single solution, and doesn't need T&E, so I would love to see your solutions.

[miroz]

8,4,2,6,3,1,9,7,5
9,6,5,2,7,8,3,1,4
3,1,7,9,5,4,6,2,8
1,9,4,8,6,2,7,5,3
6,7,3,1,4,5,2,8,9
5,2,8,3,9,7,1,4,6
7,5,9,4,1,6,8,3,2
2,3,1,5,8,9,4,6,7
4,8,6,7,2,3,5,9,1

Forward Ariadne's thread: 151,186 back steps, time: 8 sec.
Backward Ariadne's thread: 23,454 forward steps, time: 1 sec.
Identical solutions

[tonyskn]

I tried to Dub the original puzzle into Pappocom Sudoku program and it failed to verify it...

[scrose]

This puzzle cannot be solved using logic. Trial and error must be used.

Sorry, but it can be solved without T&E. It needs three forcing chains though, which I don't think rubylips has implemented.

Oh my, that post of mine is a blast from the past! Indeed, a few of my early posts are overly assertive, and looking at them now (having accumulated some wisdom since then, I hope) makes me cringe a little.

Nevertheless, I think can defend my claim based on the time it was made. I made that post (on 2 June) some time before xy-wings had been discussed (on 24 June) and only a day following (what seems to be) the first mention of forcing chains (on 1 June). So in my defence, at the time, it certainly appeared that a guess was needed (as Animator agreed).

While it is remarkable that the grid can be solved using forcing chains or xy-wings, I would tend to agree with rafowell's astute observation; the simplest explanation is often the right one.

I tried to Dub the original puzzle into Pappocom Sudoku program and it failed to verify it...

Did you try dubbing the puzzle with a 6 at r2c2, as suggested by rafowell? The Pappocom software verifies the grid below as "hard".

Code: Select all

 . 4 2 | . 3 . | . . .
 . 6 5 | . . . | . . .
 . . . | 9 . . | . . 8
-------+-------+-------
 1 . . | 8 . . | . . .
 . . 3 | . 4 . | 2 . .
 . . . | . . 7 | . . 6
-------+-------+-------
 7 . . | . . 6 | . . .
 . . . | . . . | 4 6 .
 . . . | . 2 . | 5 9 .

[fizx1]

Here are two possible solutions, although there are more.

842 631 975
965 278 314
317 954 628

194 862 753
673 145 289
528 397 146

759 416 832
231 589 467
486 723 591,


642 138 975
985 674 712
371 952 648

127 863 954
863 145 279
594 297 186

759 416 323
238 589 467
486 321 597,


Like I said, there are more than these two, I just hate typing them in like this. I have the most advanced methods/program out there I believe--my program can solve any Sudoku. I don't want to release them just yet since I'm a poor college student and would like to make a couple bucks off the discoveries.

[scrose]

Your first solution is correct. Your second solution is invalid; among other mistakes, you have two 7's in box 9. You might want to double-check that advanced program of yours... Make sure it follows the rule of sudoku.

[miroz]

To fizx1:

It seems your "advanced methods" program checks only rows. You have multiple doubles in multiple columns (8 in second column, 7 in ninth column) and in multiple boxes (7 in third box, 8 in seventh box) for your second "solution". As I mentioned earlier, there is only one solution:

8,4,2,6,3,1,9,7,5,
9,6,5,2,7,8,3,1,4,
3,1,7,9,5,4,6,2,8,
1,9,4,8,6,2,7,5,3,
6,7,3,1,4,5,2,8,9,
5,2,8,3,9,7,1,4,6,
7,5,9,4,1,6,8,3,2,
2,3,1,5,8,9,4,6,7,
4,8,6,7,2,3,5,9,1,

Solution 1 - forward Ariadne's thread: 151,186 back steps, time: 8 sec.
Solution 2 - backward Ariadne's thread: 23,454 forward steps, time: 1 sec.
Solution 3 - backward Ariadne's thread with reversed search sequence: 584,249 forward steps, time: 35 sec.
Solution 4 - forward Ariadne's thread with reversed search sequence: 180,907 back steps, time: 11 sec.
All solutions are identical