The New Sudoku Players' Forum

[Tobymorton]

Hi
I really hope someone can help.
I am trying to improve my skills at solving super fiendish puzzles. So have been learning about X wings/Swordfish and XY wing methods.
However on the attached puzzle I just cannot see what to do next! I have entered the possible numbers in each empty cell and am sure the answer is just starring at me!
Please could someone explain to me what I am missing to solve the log jam
I will be eternally grateful as I have been trying to solve this for what seems like days
Many many thanks in anticipation
Toby Morton - UK

[pjb]

Dear Toby

Your grid is correct after removing basic set of eliminations. You now need an advanced method such as XY chain or X-wing or ALS. The 4 member XY chain:
(2=3)r5c8 - (3=9)r5c2 - (9=4)r7c2 - (4=2)r7c9 => -2 r5c9
reduces the puzzle to the point where it solves with naked and hidden singles.

Phil

[Tobymorton]

Hi Phil
Many thanks for the reply!
Looks like I have some more work to do on master these techniques.
Could you possible recommend a good article that clearly explains these advanced chain correlations
Thanks again
Toby

[Kozo Kataya]

i would like to propose another idea to solve the puzzle .
line-format: 3.......8.2.....1...16523....25936....4...8....62.49....81357...5.....8.6.......9

Code: Select all

| 3    6    5 | 49  147 19 | 24   247  8  |
| 47   2    9 | 3   47  8  | 5    1    6  |
| 478  478  1 | 6   5   2  | 3    9    47 |
|-------------+------------+--------------|
| 178  178  2 | 5   9   3  | 6    47   147|
| 59   39   4 | 7   16  16 | 8    23   25 |
| 157  137  6 | 2   8   4  | 9    37   157|
|-------------+------------+--------------|
| 249  49   8 | 1   3   5  | 7    6    24 |
| 124  5    7 | 49  246 69 | 124  8    3  |
| 6    14   3 | 8   24  7  | 124  5    9  |


Code: Select all

cells including both 4 and 7

|             |     47     |      47      | 
| 47          |     47     |              |
| 47   47     |            |           47 |
|-------------+------------+--------------|
|             |            |      47   47 |
|             |            |              |
|             |            |              |
|-------------+------------+--------------|



From a symmetrical view of [ 47 ], r1c5,r1c8,r3c2 and r4c9 might be [ 47 ] .
if so, the puzzle can be solved.
Regards

[SpAce]

Could you possible recommend a good article that clearly explains these advanced chain correlations

Some general chaining concepts (including XY-Chains): http://hodoku.sourceforge.net/en/tech_chains.php
XY-Chains specifically: http://www.sudokuwiki.org/XY_Chains
Alternating Inference Chains (AIC): http://forum.enjoysudoku.com/an-aic-primer-t33934.html

The 4 member XY chain:
(2=3)r5c8 - (3=9)r5c2 - (9=4)r7c2 - (4=2)r7c9 => -2 r5c9

Phil's XY-Chain is one kind of an AIC. The basic idea of any AIC is that it establishes a derived OR-relationship (strong link) between the two end candidates (or nodes to be more general), which means that at least one of them has to be true. Thus any other candidate that (if true) would force both of those ends to be false, i.e. has a weak link with both of them, can be eliminated. An AIC has alternating strong and weak links, with strong links at both ends. In the Eureka chain notation which is mostly used here as in Phil's example, the strong links are marked with "=" and weak links with "-". All strong links in a pure XY-Chain are bivalue cells, i.e. cells with just two candidates left.

Phil's chain proves that either the cell in [row 5, column 8] must be 2 or the cell in [row 7, column 9] must be 2 (or both); thus there can be no 2 in [row 5, column 9]. You can check the result by trying what would happen if you placed 2r5c9: it would cause a contradiction.