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11 Jan 2007 Nightmare: Unique Naked Quint

 
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Ron Moore
Addict
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Joined: 13 Aug 2006
Posts: 72
Location: New Mexico

PostPosted: Thu Jan 11, 2007 4:57 pm    Post subject: 11 Jan 2007 Nightmare: Unique Naked Quint Reply with quote

This is the position in the 11 Jan 2007 Nightmare, after initial eliminations from basic techniques, and a "128" naked triple in r2c123:

Code:
.---------------------.-------------------------.---------------------.
| 9      7      4     | 25      1258     1258   | 35     3568   2368  |
| 28     12     18    | 3       45       6      | 7      59     49    |
|*36    *36     5     | 24      7        9      | 14     18     248   |
:---------------------+-------------------------+---------------------:
| 1      8      2     | 5679    569      35     | 359    4      379   |
|*36+57 *36+59 #379   | 24-579  124-589  12-358 |#359   #35789 #3789  |
| 357    4      379   | 579     589      358    | 6      2      1     |
:---------------------+-------------------------+---------------------:
| 2457   259    79    | 1       3        25     | 8      679    4679  |
| 2345   12359  6     | 8       25       7      | 1349   139    349   |
| 378    13     1378  | 69      69       4      | 2      137    5     |
'---------------------'-------------------------'---------------------'

-
Here there is a "379" naked triple in r567c3, but it's more interesting if we ignore this, and the subsequent basic eliminations, in order to preserve the UR pattern based on "36" in r35c12 (marked with "*" in the diagram). In this pattern the surplus candidates 5,7,9 are located in row 5 only, and these form a "unique naked quint" of digits "35789" with cells r5c3789 (marked with "#" in the diagram). This results in the eliminations shown in r5c456. (Here I'm following the convention of listing all eliminated candidates to the right of the "-" sign, as I probably should have been doing all along.)

After these eliminations and basic follow-up, we can continue basically as the Sudocue solver does, using the "69" UR pattern in r49c45 and eventually an XY wing in r8c1|r29c2. (We still don't need the "379" naked triple mentioned earlier, nor the "359" naked triple in r145c7 in the diagrammed position.)
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Para
Yokozuna
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Joined: 08 Nov 2006
Posts: 384
Location: The Netherlands

PostPosted: Fri Jan 12, 2007 10:07 am    Post subject: Hidden triple? Reply with quote

Hi

Code:

.---------------------.-------------------------.---------------------.
| 9      7      4     | 25      1258     1258   | 35     3568   2368  |
| 28     12     18    | 3       45       6      | 7      59     49    |
|*36    *36     5     | 24      7        9      | 14     18     248   |
:---------------------+-------------------------+---------------------:
| 1      8      2     | 5679    569      35     | 359    4      379   |
|*36+57 *36+59 #379   | 24-579  124-589  12-358 |#359   #35789 #3789  |
| 357    4      379   | 579     589      358    | 6      2      1     |
:---------------------+-------------------------+---------------------:
| 2457   259    79    | 1       3        25     | 8      679    4679  |
| 2345   12359  6     | 8       25       7      | 1349   139    349   |
| 378    13     1378  | 69      69       4      | 2      137    5     |
'---------------------'-------------------------'---------------------'


Isn't that just a hidden triple 124 in R5C456?
I was just wondering cause it seems like going a bit on a detour with the naked quint. It kinda feels like calling an XY-wing an ALS-xz.

greetings

Para
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