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Vanhegan extreme

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Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Wed Nov 26, 2008 4:43 pm Post subject: Vanhegan extreme

Puzzle 6-625372, rated 2.1.0.1.1

If anyone wants to take a shot at this, I'd be interested to see what's there. I found nothing and had to use a couple of rounds of Medusa.

Code:

+-------+-------+-------+
| . . 7 | . 4 . | 9 . . |
| . 8 . | 1 . . | . . . |
| 4 2 . | 5 . 9 | . . . |
+-------+-------+-------+
| . . 5 | . . 4 | . . . |
| 7 1 8 | . . . | 6 2 4 |
| . . . | 8 . . | 5 . . |
+-------+-------+-------+
| . . . | 6 . 2 | . 8 9 |
| . . . | . . 1 | . 6 . |
| . . 3 | . 9 . | 1 . . |
+-------+-------+-------+

Play this puzzle online at the Daily Sudoku site

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Wed Nov 26, 2008 6:12 pm Post subject:

Code:

.------------------------.------------------------.------------------------.
| 1356 356 7 | 23 4 368 | 9 135 123568 |
| 3569 8 69 | 1 2367 367 | 2347 3457 23567 |
| 4 2 16 | 5 3678 9 | 378 137 13678 |
:------------------------+------------------------+------------------------:
| 2369 369 5 | 27 1267 4 | 378 1379 1378 |
| 7 1 8 | 9 35 35 | 6 2 4 |
| 2369 3469 2469 | 8 1267 67 | 5 1379 137 |
:------------------------+------------------------+------------------------:
| 15 457 14 | 6 357 2 | 347 8 9 |
| 2589 4579 249 | 347 3578 1 | 2347 6 2357 |
| 2568 4567 3 | 47 9 578 | 1 457 257 |
'------------------------'------------------------'------------------------'

1. (2)r1c4 = (2-8)r1c9 = (8)r1c6 - (8)r9c6 = (8-2)r9c1 = (2)r9c9 - (2)r8c7 = (2)r2c7; r2c5 <> 2
2. XYZ - wing {1,3,5} in box 1

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Wed Nov 26, 2008 9:16 pm Post subject:

Code:

+--------------------------------------------------------------------------------+
| 1356 356 7 | 23 4 368 | 9 135 123568 |
| 3569 8 69 | 1 2367 367 | 2347 3457 23567 |
| 4 2 16 | 5 3678 9 | 378 137 13678 |
|--------------------------+--------------------------+--------------------------|
| 2369 369 5 | 27 1267 4 | 378 1379 1378 |
| 7 1 8 | 9 35 35 | 6 2 4 |
| 2369 3469 2469 | 8 1267 67 | 5 1379 137 |
|--------------------------+--------------------------+--------------------------|
| 15 457 14 | 6 357 2 | 347 8 9 |
| 2589 4579 249 | 347 3578 1 | 2347 6 2357 |
| 2568 4567 3 | 47 9 578 | 1 457 257 |
+--------------------------------------------------------------------------------+
# 122 eliminations remain

Code:

1) Sometimes, extending an AIC into a non-AIC is useful.

extended | ----------------- AIC ---------------- |
[r1c9]=2 => [r9c9]=2=[r9c1]=8=[r9c6]-8-[r1c6]=8=[r1c9] => [r1c9]<>2

2) Same XYZ-Wing as Norm.

Sorry, but NL notation seems the most comfortable for me here.

Asellus

Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

Posted: Wed Nov 26, 2008 10:15 pm Post subject:

daj95376 wrote:

Sometimes, extending an AIC into a non-AIC is useful.

Your elimination is an AIC:
(2)r1c9 - (2)r9c9=(2-8)r9c1=(8)r9c6 - (8)r1c6=(8-2)r1c9; r1c9<>2

In NL:
[r1c9]-2-[r9c9]=2=[r9c1]=8=[r9c6]-8-[r1c6]=8=[r1c9] => [r1c9]<>2

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Thu Nov 27, 2008 2:49 am Post subject:

Asellus wrote:

daj95376 wrote:

Sometimes, extending an AIC into a non-AIC is useful.

Your elimination is an AIC:
(2)r1c9 - (2)r9c9=(2-8)r9c1=(8)r9c6 - (8)r1c6=(8-2)r1c9; r1c9<>2

In NL:
[r1c9]-2-[r9c9]=2=[r9c1]=8=[r9c6]-8-[r1c6]=8=[r1c9] => [r1c9]<>2

The last time I looked, the green logic represents weak inference ... and prohibits the chain from being an AIC.

Asellus

Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

Posted: Thu Nov 27, 2008 4:09 am Post subject:

daj95376 wrote:

The last time I looked, the green logic represents weak inference ... and prohibits the chain from being an AIC.

Not at all. It is an AIC loop with a weak link discontinuity. (2)r1c9 is weakly linked to the <8> in the same cell and to the <2> at r9c9. These in turn are strongly linked by the AIC. The Nice Loop convention of linking "cells" rather than candidate digits obscures this, perhaps. Clearly notated discontinuous AIC loops always begin and end with the items at the discontinuity. Some people omit the discontinuity in their notation, but it is there nonetheless.

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Thu Nov 27, 2008 5:31 am Post subject:

Asellus wrote:

Not at all. It is an AIC loop with a weak link discontinuity.

Yes

I'd drilling the basic AIC rules into my head, and I'm still adjusting to the concept of an AIC loop with a weak link. Given my failing memory anymore, odds are that I'll repeat this mistake. Sorry Exclamation

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