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 Post subject: Need help.
PostPosted: Tue Feb 10, 2009 8:14 pm 
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Grand Master
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Posts: 868
I need help with the following puzzle:

Image

006000207000070050002500004005040001900306005400010300500002400060090000103000900



Using only Basic Techniques (N/H-Subsets and Intersections) I can solve this puzzle as far as follows:
Image
Code:
+----------------------+----------------------+----------------------+
| 38     5      6      | 14     38     14     | 2      9      7      |
| 38     14     14     | 2      7      9      | 6      5      38     |
| 7      9      2      | 5      6      38     | 1      38     4      |
+----------------------+----------------------+----------------------+
| 6      3      5      | 9      4      78     | 78     2      1      |
| 9      178    178    | 3      2      6      | 78     4      5      |
| 4      2      78     | 78     1      5      | 3      6      9      |
+----------------------+----------------------+----------------------+
| 5      78     9      | 178    38     2      | 4      1378   6      |
| 2      6      478    | 1478   9      13478  | 5      1378   38     |
| 1      478    3      | 6      5      478    | 9      78     2      |
+----------------------+----------------------+----------------------+

To complete the puzzle I need two Advanced Techniques plus Basic Techniques.
Almost any combination of two Advanced Techniques cracks the puzzle.
Here are a couple of possibilities:
Hidden Text:
Image



Image

What I am trying to figure out is if it is possible to solve this puzzle using a single Advanced Technique only, plus Basic Techniques.
My analysis (which could be flawed) concludes that to solve the puzzle using a single Advanced Technique only, this technique must determine the solution for one of the eight green coloured cells, which all takes either the digit 7 or 8 as its solution.

Any bright ideas?

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 Post subject: Re: Need help.
PostPosted: Fri Feb 13, 2009 8:25 pm 
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Grand Master
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Joined: Tue Aug 05, 2008 11:43 am
Posts: 246
I couldn't find the desired step.

Børge,
The Players' forum has many players who solve even the impossible ones manually. I'm sure you'll find your answer there.

tarek


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 Post subject: Re: Need help.
PostPosted: Fri Sep 03, 2010 1:16 am 
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Posts: 6
..6...2.7....7..5...25....4..5.4...19..3.6..54...1.3..5....24...6..9....1.3...9..

after applying singles
Code:
38 ```5 ```6 | 1489 38 13489 | `2 ``389 ``7
38 1489 1489 | ```2 `7 13489 | `6 ````5 389
`7 ``89 ```2 | ```5 `6 ``389 | `1 ``389 ``4
-------------+---------------+--------------
`6 ```3 ```5 | `789 `4 ``789 | 78 ````2 ``1
`9 `178 `178 | ```3 `2 ````6 | 78 ````4 ``5
`4 ```2 ``78 | `789 `1 ````5 | `3 `6789 689
-------------+---------------+--------------
`5 `789 `789 | 1678 38 ````2 | `4 13678 368
`2 ```6 `478 | 1478 `9 13478 | `5 `1378 `38
`1 `478 ```3 | 4678 `5 ``478 | `9 ``678 ``2


naked pair r1.15 {38}.468// in row 1, col's 1 and 5 the naked pair {38} preempts the same candidates from r1c4, r1c6 and r1c8

assert singles again

Code:
38 ```5 ```6 | ``14 38 ```14 | `2 ```9 `7
38 1489 1489 | ```2 `7 13489 | `6 ```5 38
`7 ``89 ```2 | ```5 `6 ``389 | `1 ``38 `4
-------------+---------------+------------
`6 ```3 ```5 | ```9 `4 ```78 | 78 ```2 `1
`9 `178 `178 | ```3 `2 ````6 | 78 ```4 `5
`4 ```2 ``78 | ``78 `1 ````5 | `3 ```6 `9
-------------+---------------+------------
`5 `789 `789 | `178 38 ````2 | `4 1378 `6
`2 ```6 `478 | 1478 `9 13478 | `5 1378 38
`1 `478 ```3 | ```6 `5 ``478 | `9 ``78 `2


naked pair r2.19 {38}.236
naked pair b1.14 {38}.8 // the positions 1 and 4 of box 1 have a naked {38}, preempting it from box 1 position 8

assert singles

Code:
38 ``5 ``6 | ``14 38 ```14 | `2 ```9 `7
38 `14 `14 | ```2 `7 ````9 | `6 ```5 38
`7 ``9 ``2 | ```5 `6 ```38 | `1 ``38 `4
-----------+---------------+------------
`6 ``3 ``5 | ```9 `4 ```78 | 78 ```2 `1
`9 178 178 | ```3 `2 ````6 | 78 ```4 `5
`4 ``2 `78 | ``78 `1 ````5 | `3 ```6 `9
-----------+---------------+------------
`5 `78 ``9 | `178 38 ````2 | `4 1378 `6
`2 ``6 478 | 1478 `9 13478 | `5 1378 38
`1 478 ``3 | ```6 `5 ``478 | `9 ``78 `2

ff {3} r1c5 % r37 > c8 // this is a sashimi fish fin, {3} cannot be in r1c5 because then rows three and seven would only have candidate {3}'s in column eight alone.

assert singles

Code:
3 ``5 ``6 | `14 8 `14 | `2 9 7
8 `14 `14 | ``2 7 ``9 | `6 5 3
7 ``9 ``2 | ``5 6 ``3 | `1 8 4
----------+-----------+--------
6 ``3 ``5 | ``9 4 `78 | 78 2 1
9 178 178 | ``3 2 ``6 | 78 4 5
4 ``2 `78 | `78 1 ``5 | `3 6 9
----------+-----------+--------
5 `78 ``9 | `78 3 ``2 | `4 1 6
2 ``6 `47 | 147 9 147 | `5 3 8
1 `48 ``3 | ``6 5 `48 | `9 7 2

naked pair c4.67 {78}.8
house innersection claim b7 {8} c2.5 // box 7 claims the {8} out of column 2 position 5 (r5c2)
ff {7} r5c2 % r67 > c4 // sashimi fish fin r5c2 cannot be {7} because rows 6 and 7 then only have candidate {7} in column 4 alone

Code:
3 `5 ``6 | 14 8 `14 | `2 9 7
8 14 `14 | `2 7 ``9 | `6 5 3
7 `9 ``2 | `5 6 ``3 | `1 8 4
---------+----------+--------
6 `3 ``5 | `9 4 `78 | 78 2 1
9 `1 178 | `3 2 ``6 | 78 4 5
4 `2 `78 | 78 1 ``5 | `3 6 9
---------+----------+--------
5 78 ``9 | 78 3 ``2 | `4 1 6
2 `6 `47 | 14 9 147 | `5 3 8
1 48 ``3 | `6 5 `48 | `9 7 2

naked singles from here to the end.


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