The New Sudoku Players' Forum

[mdelgado]

I'd like to use some of the advanced techniques (X-Wing, Swordfish, coloring etc..) in my Sudoku solving. Problem is that I don't know how to identify them. I have the following difficult Sudoku. Can you help? (It might note even call for advanced techniques). Thanks.

9XX X61 85X
XXX XXX 96X
6X4 9XX 127

X86 492 5X1
129 357 486
54X 816 X92

29X XXX 6X8
X65 XXX XX9
XXX 679 2X5

[Sped]

Once you progress to this:

Code: Select all

 
 *-----------------------------------------------------------*
 | 9     37    23    | 27    6     1     | 8     5     4     |
 | 8     17    12    | 257   24    45    | 9     6     3     |
 | 6     5     4     | 9     38    38    | 1     2     7     |
 |-------------------+-------------------+-------------------|
 | 37    8     6     | 4     9     2     | 5     37    1     |
 | 1     2     9     | 3     5     7     | 4     8     6     |
 | 5     4     37    | 8     1     6     | 37    9     2     |
 |-------------------+-------------------+-------------------|
 | 2     9     137   | 15    34    345   | 6     1347  8     |
 | 347   6     5     | 12    2348  348   | 37    1347  9     |
 | 34    13    8     | 6     7     9     | 2     134   5     |
 *-----------------------------------------------------------*


There is a coloring oportunity on 7s.

If two and only two cells in a group have 7s as candidates, then those two cells form a "conjugate pair". One of the cells must be 7 and the other must not be a 7. The trick is to figure out which is which.

Start at r4c1 and label conjugate pairs of 7s alternately A and B, like this:

Code: Select all

 *-----------------------------------------------------------*
 | 9     37    23    | 27    6     1     | 8     5     4     |
 | 8     17    12    | 257   24    45    | 9     6     3     |
 | 6     5     4     | 9     38    38    | 1     2     7     |
 |-------------------+-------------------+-------------------|
 | 37A   8     6     | 4     9     2     | 5     37B   1     |
 | 1     2     9     | 3     5     7     | 4     8     6     |
 | 5     4     37B   | 8     1     6     | 37A   9     2     |
 |-------------------+-------------------+-------------------|
 | 2     9     137A  | 15    34    345   | 6     1347B 8     |
 | 347B  6     5     | 12    2348  348   | 37B   1347  9     |
 | 34    13    8     | 6     7     9     | 2     134   5     |
 *-----------------------------------------------------------*


The conjugate pairs are:

r4c1(A) and r4c8(B) in row 4
r4c8(B) and r6c7(A) in box 6
r6c7(A) and r6c3(B) in row 6
r6c3(B) and r7c3(A) in column 3
r7c3(A) and r7c8(B) in row 7
r6c7(A) and r8c7(B) in column 7
r7c3(A) and r8c1(B) in box 7

Either all the As are 7s or all the Bs are 7s.

You'll notice that the Bs share a group in row 8, also in column 8 and box 9. Since any group cannot have more than one 7, Bs cannot be 7s. So eliminate 7s from all the Bs, and set all the As to 7. The puzzle is solved.

[re'born]

Here is an alternative that might be easier to spot, depending on what your accustomed to look for.

Code: Select all

  *-----------------------------------------------------------*
 | 9     37    23    | 27    6     1     | 8     5     4     |
 | 8     17    12    | 257   24    45    | 9     6     3     |
 | 6     5     4     | 9     38    38    | 1     2     7     |
 |-------------------+-------------------+-------------------|
 |*37    8     6     | 4     9     2     | 5     37    1     |
 | 1     2     9     | 3     5     7     | 4     8     6     |
 | 5     4    *37    | 8     1     6     |*37    9     2     |
 |-------------------+-------------------+-------------------|
 | 2     9     137   | 15    34    345   | 6     1347  8     |
 |-347   6     5     | 12    2348  348   |*37    1347  9     |
 | 34    13    8     | 6     7     9     | 2     134   5     |
 *-----------------------------------------------------------*


The cells in r4c1 and r8c7 form a remote naked pair. Therefore we can eliminate 3 and 7 from any cell which sees both. In this case, we conclude that r8c1 = 4. From here, it should be all singles. Incidentally, like Sped's solution, remote naked pairs are just a special case of coloring. In this case, you do it on two digits simultaneously.

[Sped]

Here is an alternative that might be easier to spot, depending on what your accustomed to look for.

Code: Select all

  *-----------------------------------------------------------*
 | 9     37    23    | 27    6     1     | 8     5     4     |
 | 8     17    12    | 257   24    45    | 9     6     3     |
 | 6     5     4     | 9     38    38    | 1     2     7     |
 |-------------------+-------------------+-------------------|
 |*37    8     6     | 4     9     2     | 5     37    1     |
 | 1     2     9     | 3     5     7     | 4     8     6     |
 | 5     4    *37    | 8     1     6     |*37    9     2     |
 |-------------------+-------------------+-------------------|
 | 2     9     137   | 15    34    345   | 6     1347  8     |
 |-347   6     5     | 12    2348  348   |*37    1347  9     |
 | 34    13    8     | 6     7     9     | 2     134   5     |
 *-----------------------------------------------------------*


The cells in r4c1 and r8c7 form a remote naked pair. Therefore we can eliminate 3 and 7 from any cell which sees both. In this case, we conclude that r8c1 = 4. From here, it should be all singles. Incidentally, like Sped's solution, remote naked pairs are just a special case of coloring. In this case, you do it on two digits simultaneously.

This requires the chain of 73 pairs r4c1-r4c8-r6c7-r8c7 (or r4c1-r6c3-r6c7-r8c7) right?

[Mike Barker]

There are many ways to solve this puzzle. Since you asked about X-wings, there are two "finned" X-wings (also refered to as fillet-o-fish). The first is

Code: Select all

+--------------+-----------------+--------------+
|   9  37   23 |   27     6    1 |   8     5  4 |
|   8  17   12 |  257    24   45 |   9     6  3 |
|   6   5    4 |    9    38   38 |   1     2  7 |
+--------------+-----------------+--------------+
| *37   8    6 |    4     9    2 |   5   *37  1 |
|   1   2    9 |    3     5    7 |   4     8  6 |
|   5   4   37 |    8     1    6 |  37     9  2 |
+--------------+-----------------+--------------+
|   2   9  137 |   15    34  345 |   6  1347  8 |
| -347  6    5 |   12  2348  348 |  37  1347  9 |
| *34 *13    8 |    6     7    9 |   2  *134  5 |
+--------------+-----------------+--------------+

allows the 3 in r8c1 to be eliminated. This is immediately followed by

Code: Select all

+--------------+-----------------+--------------+
|   9  37   23 |   27     6    1 |   8     5  4 |
|   8  17   12 |  257    24   45 |   9     6  3 |
|   6   5    4 |    9    38   38 |   1     2  7 |
+--------------+-----------------+--------------+
| *37   8    6 |    4     9    2 |   5   *37  1 |
|   1   2    9 |    3     5    7 |   4     8  6 |
|   5   4   37 |    8     1    6 |  37     9  2 |
+--------------+-----------------+--------------+
|   2   9 *137 |   15    34  345 |   6 *1347  8 |
|  -47  6    5 |   12  2348  348 |  37  1347  9 |
|  34  13    8 |    6     7    9 |   2   134  5 |
+--------------+-----------------+--------------+

which eliminates the 7 from r8c1. Two steps as opposed to rep'nA's one with remote naked pairs, but another approach. As far as descriptions for these techniques you can look at

http://www.sadmansoftware.com/sudoku/techniques.htm
http://www.angusj.com/sudoku/hints.php
http://homepages.cwi.nl/~aeb/games/sudoku/
http://www.sudoku.org.uk/
http://www.scanraid.com/AdvanStrategies.htm

For references to advanced techniques described in this forum, I'm partial to http://forum.enjoysudoku.com/viewtopic.php?p=21804#p21804 for some reason.

[TKiel]

From the point at which mdelgado posted the puzzle, using multiple colouring on digit 7 solves the puzzle.

Tracy

[re'born]

This requires the chain of 73 pairs r4c1-r4c8-r6c7-r8c7 (or r4c1-r6c3-r6c7-r8c7) right?

Yes. I had the second one in mind, but your first chain is just as valid.