leads to a contradiction

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leads to a contradiction

Postby jayal » Thu Jan 26, 2006 11:56 pm

copy of an "evil" puzzle with my contributions

3** 856 721
186 792 453
572 134 **8

**7 963 2*5
23* 587 *4*
6** 421 3*7

7** 64* 83*
*** 31* *7*
9*3 278 ***

next, interesting clue from an online solver

"cell 9/2 is one of two candidates for 4 in R9
9/2 = 4, leads to a contradiction, so 9/9 = 4"

alternatively, 4/1 & 8/1 are the only cells with candidates 4 & 8
4/1 = 8 leads to a contradiction, so 8/1 = 8

i was confused re logic months ago & you know, somehow, something still doesn't seem "right!"
jayal
 
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Postby tarek » Fri Jan 27, 2006 12:14 am

Hi Jayal,

Does the solver employ XY wing..............

The key step in solving this would be assuning you used all basic techniques is:
Code: Select all
*--------------------------------------------------------*
| 3     49    49   | 8     5     6    | 7     2     1    |
| 1     8     6    | 7     9     2    | 4     5     3    |
| 5     7     2    | 1     3     4    | 69    69    8    |
|------------------+------------------+------------------|
| 48    14    7    | 9     6     3    | 2     18    5    |
| 2     3     19   | 5     8     7    | 169   4     69   |
| 6     59    589  | 4     2     1    | 3     89    7    |
|------------------+------------------+------------------|
| 7     125   15   | 6     4     59   | 8     3     29   |
| 48    2456  458  | 3     1     59   | 569   7     2469 |
| 9     456   3    | 2     7     8    | 156   16    46   |
*--------------------------------------------------------*
Eliminating 9 From r1c3 (4 & 1 in r4c2 form an XY wing with 9 in r1c2 & r5c3)
Eliminating 9 From r6c2 (4 & 1 in r4c2 form an XY wing with 9 in r1c2 & r5c3)


& this solves the puzzle....

If you posted your original puzzle & Pencilmarks then it would be easier to assist.

The method that you described above is a contradiction elimination (i.e. Guess "also called Trial & Error")

Tarek
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Postby TKiel » Fri Jan 27, 2006 3:51 pm

Could r5c3 (1,9), r6c2 (5,9) and r7c3 91,5) also be an xy-wing that eliminates both 5 and 9 from r6c3, leaving the 8 as the only candidate?

I think I understand how xy-wings work but I have a real hard time spotting one that makes an elimation. Is it usually just a matter of trying to see if a particular cell has wings and then checking to see if that makes an elimination (which can be quite time consuming, especially in a puzzle like this, since it has so many bivalue cells from which to choose) or is there an easier way to spot them?

Tracy
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Postby tarek » Fri Jan 27, 2006 4:23 pm

TKiel wrote:Could r5c3 (1,9), r6c2 (5,9) and r7c3 91,5) also be an xy-wing that eliminates both 5 and 9 from r6c3, leaving the 8 as the only candidate?


Hi Tracy,

Yes it is an xy wing that eliminates only 5s (as Z=5), You combine it with the other xy wing to achieve 5,9 eliminations.

However you need only one xy wing to solve this particular puzzle

Tarek
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Postby TKiel » Fri Jan 27, 2006 9:24 pm

Tarek,
You wrote:
Yes it is an xy wing that eliminates only 5s (as Z=5),
Does that mean that an xy wing can only eliminate one candidate (the Z) from any and all cells that 'see' both branches of the Y?

From the grid in your first post in this thread, we have an xy wing with r5c3 (1,9), r4c2 (1,4) and r1c3 (4,9) which would eliminate 4 in r1c2. Since, an xy wing is sort of a naked triple (in that the 3 candidates must be in the 3 cells in some order) and both candidate 9's in the xy wing are contained in column 3, couldn't we also eliminate 9 as a candidate from all cells in column 3 that are not part of the xy wing?

Tracy
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leads to a contradiction

Postby jayal » Fri Jan 27, 2006 10:16 pm

thanks for your reply "tarek" - i copied the puzzle from "websudoku.com" and don't usually keep a record, the "solver" is at "sudokusourceforge.net" - it verifies a true sudoku then will solve and note the patterns used to solve - these do include xwing, swordfish, nishio and "guess" - still trying to figure, eg, how to eliminate that 9 in r3, then xwings are also dificult to spot
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Postby tarek » Sat Jan 28, 2006 12:48 am

TKiel wrote:From the grid in your first post in this thread, we have an xy wing with r5c3 (1,9), r4c2 (1,4) and r1c3 (4,9) which would eliminate 4 in r1c2. Since, an xy wing is sort of a naked triple (in that the 3 candidates must be in the 3 cells in some order) and both candidate 9's in the xy wing are contained in column 3, couldn't we also eliminate 9 as a candidate from all cells in column 3 that are not part of the xy wing?

THe XY wing eliminates Candidate Z from cells that "See" both XZ & YZ cells......

if XZ sees YZ Then it is a special condition similar to the Naked Triple....
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