11 Jan 2007 Nightmare: Unique Naked Quint
Posted: Thu Jan 11, 2007 4:57 pm
This is the position in the 11 Jan 2007 Nightmare, after initial eliminations from basic techniques, and a "128" naked triple in r2c123:
-
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.)
Code: Select all
.---------------------.-------------------------.---------------------.
| 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.)