SudoCue Users
A forum for users of the SudoCue programs and the services of SudoCue.Net

Author Message
Ron Moore

Joined: 13 Aug 2006
Posts: 72
Location: New Mexico

Posted: Thu Dec 14, 2006 4:51 pm    Post subject: 5 Dec 2006 Nightmare: No Medusa Bridges Needed

I was able to solve the 5 Dec Nightmare without using Medusa bridges or 3-D chains. This is the position after eliminations from basic techniques, a naked "238" triple in r12c9|r3c7, and an empty rectangle for digit "9" in box 6, eliminating (9)r9c8.
 Code: .------------------.------------------.------------------. | 2    A34    7    | 6    -3489  489  | 5     1    D38   | | 68    13-45 45   | 23    12348 7    | 9     46    23-8 | | 68    13-4   9   | 5     12348 1248 | 28    46    7    | :------------------+------------------+------------------: | 5     6     2    | 19    179   3    | 178   89    4    | | 79    8     13   | 4     5     6    | 127   239   129  | | 4     79    13   | 8     1279  129  | 6     39    5    | :------------------+------------------+------------------: | 1     79    6    | 23    2389  5    | 4     2789 C289  | | 3    B45    8    | 7     6     249  |C12   C259  C129  | | 79    2     45   | 19    1489  1489 | 3     578   6    | '------------------'------------------'------------------'

Here we have an ALS ring (generalization of an XY ring), with nodes marked with letters A thru D. Node C is the only grouped node. In AIC form:

(3=4)r1c2 - (4=5)r8c2 - (5=1298)r7c9|r8c789 - (8=3)r1c9 - (3=4)r1c2

The ring gives eliminations of (4)r23c2, (8)r2c9, and (3)r1c5. After these eliminations and basic follow-up the grid looks like this:
 Code: .------------------.------------------.------------------. | 2     34    7    | 6  *489   *489   | 5     1     *38  | | 68    15    45   | 23  148    7     | 9     46    *23  | |*68    13    9    | 5   123-48 12-48 |*28   *46     7   | :------------------+------------------+------------------: | 5     6     2    | 19  179    3     | 178   89    4    | | 79    8     13   | 4   5      6     | 127   239   129  | | 4     79    13   | 8   1279   129   | 6     39    5    | :------------------+------------------+------------------: | 1     79    6    | 23  2389   5     | 4     2789  289  | | 3     45    8    | 7   6      249   | 12    259   129  | | 79    2     45   | 19  1489   1489  | 3     578   6    | '------------------'------------------'------------------'

There is a grouped chain (marked with "*") which eliminates (4)r3c56:

(4=682)r3c178 - (2=38)r12c9 - (8=94)r1c56 => r3c56 <> 4

This leaves r3c8 as the only cell with a "4" candidate in row 3. Following up we reach:
 Code: .---------------.---------------.---------------. | 2    34   7   | 6    489  489 | 5    1    38  | | 8    15   45  | 23   14   7   | 9    6    23  | | 6    13   9   | 5    1238 128 | 28   4    7   | :---------------+---------------+---------------: | 5    6    2   | 19   179  3   | 178  89   4   | |#79   8    13  | 4    5    6   |*12+7 239 *12+9| | 4   #79   13  | 8    1279 129 | 6    39   5   | :---------------+---------------+---------------: | 1   #79   6   | 23   2389 5   | 4    2789 28-9| | 3    45   8   | 7    6    249 |*12   259 *12+9| | 79   2    45  | 19   1489 1489| 3    578  6   | '---------------'---------------'---------------'

To avoid a rectangular deadly pattern of "12" cells in r58c79 (marked with "*"), either a "9" must be placed in one of r58c9, or a "7" must be placed in r5c7. In the latter case, there is a short chain (marked with "#") which results in r7c2=9, so that in both cases r7c9 sees a "9". In AIC form:

(9=12)r58c9 - UR - (12=7)r58c7 - (7=9)r5c1 - (9=7)r6c2 - (7=9)r7c2 => r7c9 <> 9

With r7c9 reduced to "28", there is now a naked "238" triple in r127c9. Following up, we find an X-wing for digit "2" in r27c49, eliminating (2)r7c58, and an XY wing eliminating (3)r6c3:

(3=1)r5c3 - (1=9)r5c9 - (9=3)r6c8 => r6c3 <> 3

This brings us to:
 Code: .---------------.---------------.------------------. | 2    34   7   | 6    489  489 | 5     1      38  | | 8    15   45  | 23   14   7   | 9     6      23  | | 6    13   9   | 5    1238 128 | 28    4      7   | :---------------+---------------+------------------: | 5    6    2   | 19   179  3   | 78    89    4    | | 79   8    3   | 4    5    6   |*12+7 *29   *19   | | 4    79   1   | 8    279  29  | 6     3     5    | :---------------+---------------+------------------: | 1    79   6   | 23   389  5   | 4     789   28   | | 3    45   8   | 7    6    249 |*12   *29+5 *19   | | 79   2    45  | 19   1489 1489| 3     578   6    | '---------------'---------------'------------------'

To avoid a deadly pattern of 12-29-91 in r58c789 (marked with "*"), either r5c7 must be "7" or r8c8 must be "5". But we can show (7)r5c7 => (5)r8c8. In the AIC below, I've used "DP" for "deadly pattern."

(5=129)r8c789 - DP - (129=7)r5c789 - (7=8)r4c7 - (8=295)r458c8 => r8c8=5

and this is enough to complete the solution easily. By comparison, from the position above the Sudocue solver uses (not in order) a Nishio step, three XY chains, a naked quad, and an XY wing to complete the solution.
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First
 All times are GMT Page 1 of 1

 Jump to: Select a forum SudoCue - the Website----------------Daily Sudoku Nightmare & ArchiveClueless SpecialsClueless ExplosionsWeekly AssassinsTexas Jigsaw KillersSudoku LiteX-FilesDaily WindokuDaily Jigsaw SudokuSolving Guide & GlossarySamurai ContestGeneral Website Comments Sudoku - the Community----------------Help Me! I'm stuck!Solving Techniques & TipsWebsitesSoftwarePuzzlesPublicationsOff-Topic SudoCue - the Software----------------SupportWishlistCommentsReleases
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum