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5 Dec 2006 Nightmare: No Medusa Bridges Needed

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

PostPosted: Thu Dec 14, 2006 4:51 pm    Post subject: 5 Dec 2006 Nightmare: No Medusa Bridges Needed Reply with quote

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.
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