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What solving techique is this?

 
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fatcatz
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PostPosted: Wed Apr 18, 2007 4:04 am    Post subject: What solving techique is this? Reply with quote

Hi

I'm using SudoCue to learn about the different solving techniques. Sometimes I come across the following "RyCx Digit z elimated by all candidates of RaCb".

Below is an example, SudoCue shows "R8C2 Digit 1 eliminated by all candidates of R7C6", can anyone tell me what techique was used as I don't understand why the candidates at R7C6 can result in the elimination of 1 at R8C2?

Code:

000070940070090005300005070087400100463080000000007080800700000700000028050268000
.------------------.------------------.------------------.
| 1256  12    1258 | 1368  7     1236 | 9     4     1236 |
| 126   7     1248 | 1368  9     12346| 2368  136   5    |
| 3     1249  1489 | 168   124   5    | 268   7     126  |
:------------------+------------------+------------------:
| 259   8     7    | 4     235   2369 | 1     3569  2369 |
| 4     6     3    | 159   8     129  | 257   59    279  |
| 1259  129   1259 | 3569  235   7    | 23456 8     23469|
:------------------+------------------+------------------:
| 8     12349 1246 | 7     1345 *1349 | 456   1569  1469 |
| 7    *1349  146  | 1359  1345  1349 | 456   2     8    |
| 19    5     149  | 2     6     8    | 347   139   13479|
'------------------'------------------'------------------'
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zoltag
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PostPosted: Wed Apr 18, 2007 4:25 am    Post subject: Reply with quote

That is a form of tabling and isn't used by humans, in general.

http://www.sudopedia.org/wiki/Tabling
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fatcatz
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PostPosted: Wed Apr 18, 2007 4:29 am    Post subject: Reply with quote

Thanks for the fast response. So to disable this solving technique (since it is not human usable) I just uncheck Table Conflict and Table Verity in SudoCue?
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zoltag
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PostPosted: Wed Apr 18, 2007 4:38 am    Post subject: Reply with quote

Yes. The verity is a method that builds several forcing chains and uses the combination to get the result. Here is the explanation for your question above, computer generated, btw.

Dynamic Cell Forcing Chains

With this solving technique, we will prove the following assertions:

If R7C6 contains the value 1, then R8C2 cannot contain the value 1
If R7C6 contains the value 3, then R8C2 cannot contain the value 1
If R7C6 contains the value 4, then R8C2 cannot contain the value 1
If R7C6 contains the value 9, then R8C2 cannot contain the value 1

Because the cell R7C6 cannot contain other values, and the results are the same, we can conclude that R8C2 cannot contain the value 1.

Each assertion is proved by a different chain of simple rules. The chains can be dynamic, which means that the conclusions of multiple sub-chains must be combined in some cases.
The details of each chain are given below.

Chain 1: If R7C6 contains the value 1, then R8C2 cannot contain the value 1

(1) If R7C6 contains the value 1, then R8C5 cannot contain the value 1 (the value can occur only once in the block)
(2) If R7C6 contains the value 1 (initial assumption), then R7C5 cannot contain the value 1 (the value can occur only once in the block)
(3) If R7C5 does not contain the value 1 and R8C5 does not contain the value 1 (1), then R3C5 must contain the value 1 (only remaining possible position in the column)
(4) If R3C5 contains the value 1, then R3C5 cannot contain the value 4 (the cell can contain only one value)
(5) If R3C5 does not contain the value 4, then R2C6 must contain the value 4 (only remaining possible position in the block)
(6) If R2C6 contains the value 4, then R2C6 cannot contain the value 2 (the cell can contain only one value)
(7) If R3C5 contains the value 1 (3), then R3C5 cannot contain the value 2 (the cell can contain only one value)
(8) If R3C5 does not contain the value 2 and R2C6 does not contain the value 2 (6), then R1C6 must contain the value 2 (only remaining possible position in the block)
(9) If R1C6 contains the value 2, then R1C2 cannot contain the value 2 (the value can occur only once in the row)
(10) If R1C2 does not contain the value 2, then R1C2 must contain the value 1 (only remaining possible value in the cell) (11) If R1C2 contains the value 1, then R8C2 cannot contain the value 1 (the value can occur only once in the column)

Chain 2: If R7C6 contains the value 3, then R8C2 cannot contain the value 1
(1) If R7C6 contains the value 3, then R8C6 cannot contain the value 3 (the value can occur only once in the block)
(2) If R7C6 contains the value 3 (initial assumption), then R8C4 cannot contain the value 3 (the value can occur only once in the block)
(3) If R7C6 contains the value 3 (initial assumption), then R8C5 cannot contain the value 3 (the value can occur only once in the block)
(4) If R8C5 does not contain the value 3, R8C4 does not contain the value 3 (2) and R8C6 does not contain the value 3 (1), then R8C2 must contain the value 3 (only remaining possible position in the row)
(5) If R8C2 contains the value 3, then R8C2 cannot contain the value 1 (the cell can contain only one value)

Chain 3: If R7C6 contains the value 4, then R8C2 cannot contain the value 1

(1) If R7C6 contains the value 4, then R8C5 cannot contain the value 4 (the value can occur only once in the block)
(2) If R7C6 contains the value 4 (initial assumption), then R7C5 cannot contain the value 4 (the value can occur only once in the block)
(3) If R7C5 does not contain the value 4 and R8C5 does not contain the value 4 (1), then R3C5 must contain the value 4 (only remaining possible position in the column)
(4) If R3C5 contains the value 4, then R3C2 cannot contain the value 4 (the value can occur only once in the row)
(5) If R7C6 contains the value 4 (initial assumption), then R7C2 cannot contain the value 4 (the value can occur only once in the row)
(6) If R7C2 does not contain the value 4 and R3C2 does not contain the value 4 (4), then R8C2 must contain the value 4 (only remaining possible position in the column)
(7) If R8C2 contains the value 4, then R8C2 cannot contain the value 1 (the cell can contain only one value)

Chain 4: If R7C6 contains the value 9, then R8C2 cannot contain the value 1

(1) If R7C6 contains the value 9, then R8C6 cannot contain the value 9 (the value can occur only once in the block)
(2) If R7C6 contains the value 9 (initial assumption), then R8C4 cannot contain the value 9 (the value can occur only once in the block)
(3) If R8C4 does not contain the value 9 and R8C6 does not contain the value 9 (1), then R8C2 must contain the value 9 (only remaining possible position in the row)
(4) If R8C2 contains the value 9, then R8C2 cannot contain the value 1 (the cell can contain only one value)
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fatcatz
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PostPosted: Wed Apr 18, 2007 5:10 am    Post subject: Reply with quote

Thanks zoltag for the answer. I wish SudoCue could show the actual method used for beginners like me. For example: "R8C2 Digit 1 eliminated by all candidates of R7C6 using Table Verity".
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zoltag
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PostPosted: Wed Apr 18, 2007 10:49 am    Post subject: Reply with quote

Beginners wouldn't be solving a puzzle this hard, very few people would.
This is the "long" description Soduko Cue provides for this step, and it is clear enough.

Code:
When any of the candidates of R7C6 is placed, this always leads to the elimination of R8C2 Digit 1.  The elimination of this candidate is therefore true under all circumstances.
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