The New Sudoku Players' Forum

[BakyX]

Hello. I need help with next move, again

[Leren]

This puzzle has multiple solutions - there is either a missing clue or one of the solved cells is in the wrong position or is the wrong number.

Leren

[JC Van Hay]

The last step you did was an XWing(6C26).
But ... this leads to only 2 solutions for the digit 6.

So, L1C5=6 -> contradiction :=> L1C3=6; 48 solved cells.

Next ... There are only 2 solutions for the digit 2.

So, whether L4C2=2 -> 71 solved cells,
and whether L5C6=9 -> the puzzle has 2 solutions; or L5C9=9 -> the puzzle has 2x2=4 solutions;

or L4C6=2 -> 50 solved cells,
and whether L3C8=4 -> the puzzle has 1 solution; or L3C9=4 -> 62 solved cells,
and whether L5C6=9 -> the puzzle has 2 solutions, or L5C9=9 -> the puzzle has 2x2=4 solutions.

Conclusion : the puzzle has 13 solutions !

[Leren]

JC Van Hay wrote : Conclusion : the puzzle has 13 solutions !

Well done ! Here are the 13 solutions (in line format) that I found in Andrew Stuart's solver.

536724198497518326281396745659872431724631859813945672972163584365489217148257963
536724198497518326281396754653172849724689531819435672172963485965847213348251967
536724198497518326281396754653271849724689531819435672172963485965847213348152967
536724198497518326281396754653279841724681539819435672172963485965847213348152967
536724198497518326281396754653972841724681539819435672972163485365849217148257963
536724198497581326281396754653279841724618539819435672172963485965847213348152967
536724198497581326281396754653972841724618539819435672972163485365849217148257963
536724891497518326281396754653279148724681539819435672172963485965847213348152967
536724891497518326281396754653972148724681539819435672972163485365849217148257963
536724891497581326281396754653278149724619538819435672172963485965847213348152967
536724891497581326281396754653279148724618539819435672172963485965847213348152967
536724891497581326281396754653872149724619538819435672972163485365948217148257963
536724891497581326281396754653972148724618539819435672972163485365849217148257963

PS : A challenge for all the puzzle creators out there. Can you produce a valid single solution puzzle from the given puzzle's solved cells by either:

1. Adding one extra clue; 2. Moving one of the solved cells to another position; or 3. Changing one of the solved cells to another digit.

Leren

[JC Van Hay]

PS : A challenge for all the puzzle creators out there. Can you produce a valid single solution puzzle from the given puzzle's solved cells by either:

1. Adding one extra clue; ...

L3C8=4 -> valid easy puzzle (-6L1C5; stte).

[Leren]

JC Van Hay wrote : L3C8=4 -> valid easy puzzle

Again well done ! Adding r3c8 = 4 as an extra clue leads to a single solution 536724198497518326281396745659872431724631859813945672972163584365489217148257963

We'll now wait with bated breath to see whether this matches BakyX's error .

Leren

[BakyX]

I'm sorry. I made a mistakes when I was transcribing the puzzle from magazine. This is already the corect one at the point where I've got stucked I hope this one has a unique solution.

[JasonLion]

Yes, this puzzle has a single solution. It is however a more complex puzzle than anything you have posted before.

The next move is either unique rectangle type 1 or a finned x-wing.

[BakyX]

"unique rectangle", you probably mean r5c8 = 9 Very nice trick

And what do you mean with "finned x-wing", please ? I've never heard about that before. In generally I don't like to read articles about solving techniques, I'd like to generalize them by myself

[JasonLion]

A finned x-wing is much like a regular x-wing, but with an extra cell containing a candidate (sharing a block with one of the x-wing cells) that would otherwise invalidate the x-wing. Either the x-wing is valid, or the extra cell contains the candidate. Either way, x-wing style eliminations made in the block containing the fin are still valid (though the other x-wing eliminations are not).

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 5     3     679    | 27    26    4      | 18    29    18     |
| 4     9-1   79     | 5     128   1278   | 3     29    6      |
| 2     68   *18     | 3     9    *16     | 7     4     5      |
|--------------------+--------------------+--------------------|
| 16    5     69     | 1289  7     1289   | 4     3     189    |
| 7     2     4      | 6     3     189    | 18    5     189    |
| 8    *19    3      | 4     5    *19     | 6     7     2      |
|--------------------+--------------------+--------------------|
| 169   7     2      | 19    16    3      | 5     8     4      |
| 39    68    5      | 789   4     6789   | 2     1     37     |
| 13    4     18     | 1278  128   5      | 9     6     37     |
*--------------------------------------------------------------*

From the position you show in your PM a Skyscraper solves the puzzle. It is shown by the cells marked *.

It works like this :There are 2 1's in Rows 3 and 6. So if r3c3 <> 1, r3c6 = 1, r6c6 <> 1, r6c2 = 1.

You can follow this in chain in reverse, the overall conclusion being that at least 1 of r3c3 and r6c2 must be 1.

Since r2c2 sees both of these cells it can't be 1, so it's 9 and the puzzle solves easily from there.

There is one slight difference between your PM and mine, I've removed 9 from r4c1 because of a pointing pair of 9's in Box 7.

Leren

[BakyX]

A finned x-wing is much like a regular x-wing, but with an extra cell containing a candidate (sharing a block with one of the x-wing cells) that would otherwise invalidate the x-wing. Either the x-wing is valid, or the extra cell contains the candidate. Either way, x-wing style eliminations made in the block containing the fin are still valid (though the other x-wing eliminations are not).

Thank you, I found some finned x-wings in this puzzle, nice and logical trick

A finned x-wing is much like a regular x-wing, but with an extra cell containing a candidate (sharing a block with one of the x-wing cells) that would otherwise invalidate the x-wing. Either the x-wing is valid, or the extra cell contains the candidate. Either way, x-wing style eliminations made in the block containing the fin are still valid (though the other x-wing eliminations are not).

Thank you, I understand I used this trick a few times in this puzzle, but not so much as it was required