The New Sudoku Players' Forum

[xatomicrenee]

I'm stuck and i'm really bad at x-wing and other techniques please help ;-;

[JasonLion]

.8.23...93.2956.879..48.3.2431895276698372.1..2.6149388..5....12..1.....16.7....3

This puzzle is a little on the complex side for someone still working on X-Wings.

The first thing I notice is a pair of unique rectangles (type 1), however they don't get you all that far. It looks like you will probably end up needing a couple of additional techniques at roughly that level before you are through.

[Leren]

Withdrawn - based on Jason's incorrect line format for the puzzle

Leren

[JC Van Hay]

Code: Select all

+----------------+-------------+-----------------+
| 57  8    4567  | 2  3    17  | 1456   456   9  |
| 3   14   2     | 9  5    6   | 14     8     7  |
| 9   157  567   | 4  8    17  | 3      56    2  |
+----------------+-------------+-----------------+
| 4   3    1     | 8  9    5   | 2      7     6  |
| 6   9    8     | 3  7    2   | 45     1     45 |
| 57  2    57    | 6  1    4   | 9      3     8  |
+----------------+-------------+-----------------+
| 8   47   3479  | 5  246  39  | 467    2469  1  |
| 2   457  34579 | 1  46   389 | 45678  4569  45 |
| 1   6    459   | 7  24   89  | 458    2459  3  |
+----------------+-------------+-----------------+

If you really want to rationally understand how to solve a puzzle, just consider as a sub-puzzle "the 3 upper boxes B123", enumerate its solutions and see what happens.

[xatomicrenee]

This was a really difficult puzzle for one from a published site. The least painful solution I could find involved 2 XYZ Wings, 5 Uniqueness moves and some intervening basics.

I can explain this in detail if you like but it will take quite a while. Well, alright here's the first 2 moves.

Code: Select all

*--------------------------------------------------------------*
|a57    8     4567   | 2     3     17     | 1456  456   9      |
| 3     14    2      | 9     5     6      | 14    8     7      |
| 9    b157   56-7   | 4     8    c17     | 3     56    2      |
|--------------------+--------------------+--------------------|
| 4     3     1      | 8     9     5      | 2     7     6      |
| 6     9     8      | 3     7     2      | 45    1     45     |
| 57    2     57     | 6     1     4      | 9     3     8      |
|--------------------+--------------------+--------------------|
| 8     47    3479   | 5     246   39     | 467   2469  1      |
| 2     457   34579  | 1     46    389    | 45678 4569  345    |
| 1     6     3459   | 7     24    389    | 458   2459  345    |
*--------------------------------------------------------------*

The cells marked a, b and c form an XYZ wing. If r3c3 = 7 then there would a would 5, c would be 1 and b would be void, so r3c3 <> 7. A pointing pair of 5's then removes 5 from r3c2.

Code: Select all

*--------------------------------------------------------------*
|*57    8    *46-57  | 2     3     17     | 1456  456   9      |
| 3     14    2      | 9     5     6      | 14    8     7      |
| 9     17    56     | 4     8     17     | 3     56    2      |
|--------------------+--------------------+--------------------|
| 4     3     1      | 8     9     5      | 2     7     6      |
| 6     9     8      | 3     7     2      | 45    1     45     |
|*57    2    *57     | 6     1     4      | 9     3     8      |
|--------------------+--------------------+--------------------|
| 8     47    3479   | 5     246   39     | 467   2469  1      |
| 2     5     3479   | 1     46    389    | 4678  469   34     |
| 1     6     349    | 7     24    389    | 458   2459  345    |
*--------------------------------------------------------------*

The cells marked * form a Unique Rectangle Type 1. If r1c3 were 5 or 7 then you would have 57 in 4 cells of a rectangle covering 2 boxes, and the puzzle solution would not be unique, so you can remove 5 and 7 from r1c3.

If you want any more let me know and I'll continue with the solution.

Leren

Yes please ;~; I'm more of a newb then I thought I was

[pjb]

Although you could start with the 2 type 1 unique rectangles and go from there, this single chain will do it.

Code: Select all

a57      8       4567   | 2      3     b17     | 1456   456    9     
 3       14      2      | 9      5      6      | 14     8      7     
 9      d17-5    567    | 4      8     c17     | 3      56     2     
------------------------+----------------------+---------------------
 4       3       1      | 8      9      5      | 2      7      6     
 6       9       8      | 3      7      2      | 45     1      45     
 57      2       57     | 6      1      4      | 9      3      8     
------------------------+----------------------+---------------------
 8       47      3479   | 5      246    39     | 467    2469   1     
 2      e457     34579  | 1      46     389    | 45678  4569   45     
 1       6       459    | 7      24     89     | 458    2459   3     


(5=7)r1c1 - (7=1)r1c6 - r3c6 = (1-5)r3c2 = r8c2, eliminating 5 from r3c2, then singles.
The logic is that if the 5 at r1c1 is true, then the 5 at r3c2 must be false. But if the 5 at r1c1 is false, then according to the chain above the 5 at r8c2 is true, again making the 5 at r3c2 false. So whether the 5 at rc1c is true or false, the 5 at r3c2 is false either way and can be eliminated.
Phil

[Leren]

Withdrawn - based on Jason's incorrect line format for the puzzle.

Leren

[Leren]

OK problem solved. I used Jason's line format for the puzzle and it has a missing clue 3 at the end.

The correct line format should be : .8.23...93.2956.879..48.3.2431895276698372.1..2.6149388..5....12..1.....16.7....3

With this additional clue the puzzle does solve in singles after the 5 has been removed from r3c2. My version of a chain that proves this is as follows :

Code: Select all

*--------------------------------------------------------------*
|a57    8     4567   | 2     3    b17     | 1456  456   9      |
| 3     14    2      | 9     5     6      | 14    8     7      |
| 9    d17-5  567    | 4     8    c17     | 3     56    2      |
|--------------------+--------------------+--------------------|
| 4     3     1      | 8     9     5      | 2     7     6      |
| 6     9     8      | 3     7     2      | 45    1     45     |
| 57    2     57     | 6     1     4      | 9     3     8      |
|--------------------+--------------------+--------------------|
| 8     47    3479   | 5     246   39     | 467   2469  1      |
| 2     457   34579  | 1     46    389    | 45678 4569  45     |
| 1     6     459    | 7     24    89     | 458   2459  3      |
*--------------------------------------------------------------*

(5=7) r1c1 - r1c6 = (7-1) r3c6 = (1) r3c2 => - 5 r3c2

What this chain says is that if r1c1 is not 5, r3c2 = 1, in particular it is not 5. Obviously if r1c1 is 5 then r3c2 is not 5.

Similar to Phil's argument, this shows that r3c2 is not 5 and the puzzle solves in singles from there.

Leren

[JasonLion]

Sorry about that. I added the trailing 3 to my post.

[Leren]

Without the 3 as a clue in r9c9 the puzzle has multiple solutions. By using 5 uniqueness arguments I picked one of these as "the" solution.

Hopefully xatomicrenee has not been too confused by all this.

As a postscript I'll suggest an alternative solution that might be easier to understand, if xatomicrenee is unfamiliar with chains.

Code: Select all

*--------------------------------------------------------------*
|a57    8     4567   | 2     3     17     | 1456  456   9      |
| 3     14    2      | 9     5     6      | 14    8     7      |
| 9    b157   56-7   | 4     8    c17     | 3     56    2      |
|--------------------+--------------------+--------------------|
| 4     3     1      | 8     9     5      | 2     7     6      |
| 6     9     8      | 3     7     2      | 45    1     45     |
| 57    2     57     | 6     1     4      | 9     3     8      |
|--------------------+--------------------+--------------------|
| 8     47    3479   | 5     246   39     | 467   2469  1      |
| 2     457   34579  | 1     46    389    | 45678 4569  45     |
| 1     6     459    | 7     24    89     | 458   2459  3      |
*--------------------------------------------------------------*

This move is called an XYZ Wing (X=1, Y=5, Z=7) : Look at the cells marked a, b and c and consider what would happen if r3c3 was 7. In that case Cell a would be 5, Cell c would be 1 and Cell b would have no candidates !

This proves that r3c3 <> 7. This then exposes a naked pair (56) in r3c38 which removes the 5 from r3c2, solving the puzzle via singles as in the other solutions.

Leren

PS I won't get caught this way again - my solver now spits the dummy if a line format input doesn't have 81 characters - don't know why I didn't think of that years ago

Leren

[JasonLion]

If you want any more let me know and I'll continue with the solution.

Leren

Yes please ;~; I'm more of a newb then I thought I was

[Leren]

xatomicrenee wrote ; Yes please ;~; I'm more of a newb then I thought I was

Hi xatomicrenee, my first post in this thread (which I've now withdrawn) was based on an incorrect transcribing of your puzzle from your picture. The clue 3 in Row 9 Column 9 was missed making the puzzle exceedingly difficult - in fact it had multiple solutions but my solver managed to pick one of them using Uniqueness moves.

Once the error was corrected I have posted two complete solutions (that both use one non-basic move followed by singles). pjb also posted a similar complete single move solution.

If you want further explanation of the posted solutions let me know.

Leren