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Puzzle NR_076

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daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Tue Oct 27, 2009 5:50 pm Post subject: Puzzle NR_076

Code:

NR puzzles can be solved using these techniques:

Basics: Naked/Hidden Single, Naked Pair/Triple, Locked Candidates 1/2
Basics+: Naked Quad, Hidden Pair/Triple/Quad
VH: BUG+1, UR Type 1, X-Wing, XY-Wing
VH+: 2-String Kite, Empty Rectangle, Remote Pair, Skyscraper,
XYZ-Wing, finned X-Wing, UR Type 2/4

Code:

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

Play this puzzle online at the Daily Sudoku site

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Tue Oct 27, 2009 9:31 pm Post subject:

continuing the chain of thought from Danny's post from here.

http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=3979

the VH path to the solution is as follows.
first grid

Code:

+-----------------+----------------+-----------+
| 6 2 7 | 9 1 8 | 3 5 4 |
| 3459 1 459 | 36 (45) 2 | 69 8 7 |
| 3459 9-45 8 | 36 7 (45) | 69 2 1 |
+-----------------+----------------+-----------+
| 2 46 46 | 5 9 7 | 8 1 3 |
| 8 579 59 | 4 3 1 | 2 79 6 |
| 79 3 1 | 2 8 6 | 4 79 5 |
+-----------------+----------------+-----------+
| 479 4679 469 | 1 2 49 | 5 3 8 |
| 1 (45) 2 | 8 (45) 3 | 7 6 9 |
| 59 8 3 | 7 6 59 | 1 4 2 |
+-----------------+----------------+-----------+

remote pair 45 eliminates the 45 from r3c2
then
second grid

Code:

+-----------------+-----------+----------+
| 6 2 7 | 9 1 8 | 3 5 4 |
| 3 1 45 | 6 45 2 | 9 8 7 |
| 45 9 8 | 3 7 45 | 6 2 1 |
+-----------------+-----------+----------+
| 2 46 46 | 5 9 7 | 8 1 3 |
| 8 (57) 59 | 4 3 1 | 2 79 6 |
| (79) 3 1 | 2 8 6 | 4 79 5 |
+-----------------+-----------+----------+
| 479 467 469 | 1 2 49 | 5 3 8 |
| 1 4-5 2 | 8 45 3 | 7 6 9 |
| (59) 8 3 | 7 6 59 | 1 4 2 |
+-----------------+-----------+----------+

xy-wing 579 removes 5 from r8c2 finishes.

BUT...

in order to back up to a step that might lead to an "almost/finned" solution that destroys the puzzle, we can't follow the above solution path,but find another...

so lets look at the second grid again.

Code:

+------------------+-------------+----------+
| 6 2 7 | 9 1 8 | 3 5 4 |
| 3 1 5(4) | 6 45 2 | 9 8 7 |
| 5(4) 9 8 | 3 7 45 | 6 2 1 |
+------------------+-------------+----------+
| 2 46 (46) | 5 9 7 | 8 1 3 |
| 8 57 59 | 4 3 1 | 2 79 6 |
| 79 3 1 | 2 8 6 | 4 79 5 |
+------------------+-------------+----------+
| 79-4 467 (469) | 1 2 (49) | 5 3 8 |
| 1 45 2 | 8 45 3 | 7 6 9 |
| 59 8 3 | 7 6 59 | 1 4 2 |
+------------------+-------------+----------+

instead of using the xy-wing
the chain marked in the grid finishes
(49)r7c36 = (6)r7c3 - (6=4)r4c3 - (4)r2c3 = (4)r3c1; r7c1 <> 4

alright, knowing that we can use this chain to solve the rest of the puzzle, we can now back up to the "first grid" to see if there is an "almost/finned" approach to this same chain.

I believe this is the gist of Danny's statement in the other post.

and we see that there is such a chain that does make this a one stepper using the chain we found in the "second grid"

Code:

+---------------------+----------------+-----------+
| 6 2 7 | 9 1 8 | 3 5 4 |
| 359(4) 1 59(4) | 36 5(4) 2 | 69 8 7 |
| 3459 59-4 8 | 36 7 45 | 69 2 1 |
+---------------------+----------------+-----------+
| 2 46 (46) | 5 9 7 | 8 1 3 |
| 8 579 59 | 4 3 1 | 2 79 6 |
| 79 3 1 | 2 8 6 | 4 79 5 |
+---------------------+----------------+-----------+
| 79-4 4679 (469) | 1 2 (49) | 5 3 8 |
| 1 5(4) 2 | 8 5(4) 3 | 7 6 9 |
| 59 8 3 | 7 6 59 | 1 4 2 |
+---------------------+----------------+-----------+

and the image.

there are many ways to write out the chain, I would write it like this.
[(49)r7c36 = (6)r7c3 - (6=4)r4c3 - (4)r2c3 = (4)r2c1] = (4)r2c5 - (4)r8c5 = (4)r8c2; r7c1 <> 4

Code:

[(49)r7c36 = (6)r7c3 - (6=4)r4c3 - (4)r2c3 = (4)r2c1]
|--------this AIC eliminates the 4 in r7c1----------|

this AIC can be seen as just another NODE in the chain

{AIC} = (4)r2c5 - (4)r8c5 = (4)r8c2

so the node can be true or false.

most importantly to understand here is regardless of whether the AIC is true or false, the 4 in r7c1 cannot exist.

I have seen this called a branced AIC, finned AIC, almost AIC, NET.

-----

the other view is

(4)r2c1
||
(4)r2c3 - (4=6)r4c3 - (6)r7c3 = (49)r7c36
||
(4)r2c5 - (4)r8c5 = (4)r8c2

and you can see with this view that the net originates off the three 4's in row 2.
exactly one of the three 4's has to be true resulting in the 4 in r7c1 being eliminated.

sorry if this isn't easy to understand the way its written here. its about as equally difficult to explain in a way that is reader friendly.

I agree with Danny that if a two step solution is found that its possible that a almost AIC might be available using the technique in the second step. you would go back to the grid prior to the first step and look for it.

tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Wed Oct 28, 2009 3:56 am Post subject:

I used a three step solution. Remote Pair 45, x-wing on 4 in r37c16, BUG+1 sets r7c1=9 A straight forward VH solution that is definitely not as interesting as the Danny/Norm approach. Ted

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Wed Oct 28, 2009 5:07 am Post subject:

tlanglet wrote:

I used a three step solution.

Remote Pair 45,
x-wing on 4 in r37c16,
BUG+1 sets r7c1=9

A straight forward VH solution that is definitely not as interesting as the Danny/Norm approach.

Ted, your solution matches the one from my solver and it was what I expected.

My recent tangent into merging steps was just for fun. As far as I'm concerned, an almost/finned solution would be a rareity. In the case of the Vanhagen puzzle, my first step was an awkward UR and it's only claim to fame was that it opened up the simpler XYZ-Wing to finish off the puzzle. It seemed reasonable to substitute an almost/finned step under such conditions.

tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Wed Oct 28, 2009 1:47 pm Post subject:

daj95376 wrote:

tlanglet wrote:

I used a three step solution.

Remote Pair 45,
x-wing on 4 in r37c16,
BUG+1 sets r7c1=9

A straight forward VH solution that is definitely not as interesting as the Danny/Norm approach.

Danny,

Given my current understanding of the process, I agree it would seem to be a lot of work to find a infrequent condition. But it could be fun also.

I remember when a finned xy-wing was a hot topic and some comments suggested it was rare, so Asellus solved a puzzle in several steps using only finned xy-wings; it was impressive.

Ted

ttt

Joined: 06 Dec 2008
Posts: 42
Location: vietnam

Posted: Wed Oct 28, 2009 3:00 pm Post subject:

daj95376 wrote:

As far as I'm concerned, an almost/finned solution would be a rarity.

I don’t think so, the reason is that we can be found another way then we would be ignored them… - esecially for Almost X-wing that sometime like Broken Wing Very Happy

.

ttt

Marty R.

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

Posted: Fri Oct 30, 2009 11:06 pm Post subject:

tlanglet wrote:

I used a three step solution.

Remote Pair 45,
x-wing on 4 in r37c16,
BUG+1 sets r7c1=9

A straight forward VH solution that is definitely not as interesting as the Danny/Norm approach.

Ted

I also started with the Remote Pairs and then the X-Wing. At that point I either didn't have or didn't see a BUG, so an XY-Wing on 694 with pincer transport finished it.

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