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sudoku.org.uk extreme #59

 
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Wed Nov 14, 2007 8:45 pm    Post subject: sudoku.org.uk extreme #59 Reply with quote

http://www.sudoku.org.uk/PrintWeeklySudoku.asp?number=59



this is the puzzle


9 x x x x 1 x x 2

x x 5 x x x 3 x x

3 x x 8 x x x x 6

x 4 x x 5 x x 9 x

1 x x x x x x x 7

x 6 x x 8 x x 4 x

5 x x 3 x 6 x x x

x x 2 x x x 6 x x

x x x x x 9 x x 8


this is as far as I can get, then it gets over my head:

9 x 6 x 3 1 x x 2

x x 5 x 6 x 3 x x

3 x x 8 x 5 x x 6

x 4 x 6 5 x x 9 x

1 5 x x x x x 6 7

x 6 9 1 8 x x 4 x

5 x x 3 x 6 x x x

x x 2 x x 8 6 x x

6 x x x x 9 x x 8


probably a variety of ALS moves and finned moves from here, and most likely a couple long chains.


and longer chains!

I can see why no one has posted any of these puzzles in the past. just way too many steps to complete them in a logical way. however, I would love to find out what others think of them

Norm
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Marty R.



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

PostPosted: Wed Nov 14, 2007 10:21 pm    Post subject: Reply with quote

I put it into grid form for those who might want to play with it.

Code:

+----------------+---------------+-----------------+
| 9    78   6    | 47   3    1   | 457  578   2    |
| 2478 1278 5    | 2479 6    247 | 3    178   149  |
| 3    127  147  | 8    2479 5   | 1479 17    6    |
+----------------+---------------+-----------------+
| 278  4    378  | 6    5    237 | 128  9     13   |
| 1    5    38   | 249  249  234 | 28   6     7    |
| 27   6    9    | 1    8    237 | 25   4     35   |
+----------------+---------------+-----------------+
| 5    1789 1478 | 3    1247 6   | 1479 127   149  |
| 47   1379 2    | 457  147  8   | 6    1357  1459 |
| 6    137  1347 | 2457 1247 9   | 1457 12357 8    |
+----------------+---------------+-----------------+

Play this puzzle online at the Daily Sudoku site
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re'born



Joined: 28 Oct 2007
Posts: 80

PostPosted: Wed Nov 14, 2007 11:50 pm    Post subject: Reply with quote

Here is an opening salvo:
Potential deadly pattern in r46c16<27> implies r4c1 = 8, r4c6 = 3 or r6c6 = 3. So we get the short AIC
(3)r46c6 = (8)r4c1 - (8=3)r5c3, => r5c6 <> 3.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Thu Nov 15, 2007 12:00 am    Post subject: Reply with quote

Sudoku Susser says it needs:

9 x Comprehensive Forcing Chains
4 x Simple Forcing Chains
1 x XYZ-Wing
6 x Intersection Removal
1 x Simple Hidden Sets
3 x Simple Naked Sets
20 x Pinned Squares

Keith
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Asellus



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

PostPosted: Thu Nov 15, 2007 8:16 am    Post subject: Reply with quote

I like re'born's UR-based AIC. Nice!

I found one that does the same without the UR:
(8=2)R5C7-(2=5)R6C7-(5={47})R1C47-(7=8)R1C2-(8=8)R7C23; R5C3<>8
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Asellus



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

PostPosted: Thu Nov 15, 2007 8:28 am    Post subject: Reply with quote

After either of the previously posted AICs, there is a {78} W-Wing in R1C2 and R4C3 that removes <7> from R3C3.

It's not that much help. The grid now looks like:
Code:
+---------------+--------------+-----------------+
| 9   78   6    | 47   3    1  | 457  578   2    |
| 478 1278 5    | 2479 6    24 | 3    178   149  |
| 3   127  14   | 8    2479 5  | 1479 17    6    |
+---------------+--------------+-----------------+
| 278 4    78   | 6    5    37 | 12   9     13   |
| 1   5    3    | 249  249  24 | 8    6     7    |
| 27  6    9    | 1    8    37 | 25   4     35   |
+---------------+--------------+-----------------+
| 5   1789 1478 | 3    1247 6  | 1479 127   149  |
| 47  1379 2    | 457  147  8  | 6    1357  1459 |
| 6   137  147  | 2457 1247 9  | 1457 12357 8    |
+---------------+--------------+-----------------+
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Thu Nov 15, 2007 9:21 am    Post subject: Reply with quote

An XYZ-wing <147> takes out <4> in R7C3.

Keith
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re'born



Joined: 28 Oct 2007
Posts: 80

PostPosted: Thu Nov 15, 2007 9:46 am    Post subject: Reply with quote

Asellus wrote:
After either of the previously posted AICs, there is a {78} W-Wing in R1C2 and R4C3 that removes <7> from R3C3.

After removing that 7, you've revealed an xyz-wing with pivot r9c3, eliminating 4 from r7c3. I then started multicoloring the numbers in the middle band which led me to this AIC:
(5)r8c9 = (5-3)r6c9 = (3)r4c9 - (3=7)r4c6 - (7=8)r4c3 - (8)r7c3 = (8-9)r7c2 = (9)r8c2, => r8c9 <> 9.
Followed by singles, which takes us to...
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re'born



Joined: 28 Oct 2007
Posts: 80

PostPosted: Thu Nov 15, 2007 9:46 am    Post subject: Reply with quote

(5)r8c9 = (5)r6c9 - (5=2)r6c7 - (2=7)r6c1 - (7=4)r8c1, => r8c9<>4

(naked triple in column 9)

I then noticed a useless wxyz-wing r2c9, r3c378 with pivot r3c7, which implies at least one of those cells is a 4. Transporting r2c9 to r3c3 via r2c1, we then get that r3c5<>4.
This takes here:
Code:
 *-----------------------------------------------------------*
 | 9     78    6     | 47    3     1     | 457   578   2     |
 | 478   1278  5     | 2479  6     24    | 3     178   49    |
 | 3     127   14    | 8     279   5     | 1479  17    6     |
 |-------------------+-------------------+-------------------|
 | 278   4     78    | 6     5     37    | 12    9     13    |
 | 1     5     3     | 249   249   24    | 8     6     7     |
 | 27    6     9     | 1     8     37    | 25    4     35    |
 |-------------------+-------------------+-------------------|
 | 5     178   18    | 3     1247  6     | 1479  127   49    |
 | 47    9     2     | 457   147   8     | 6     3     15    |
 | 6     3     147   | 2457  1247  9     | 1457  1257  8     |
 *-----------------------------------------------------------*
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Asellus



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

PostPosted: Thu Nov 15, 2007 10:09 am    Post subject: Reply with quote

Yeah... well while you were doing all that, I found a way to get rid of <7> in R4C1 by exploiting the strong inferential link between the W-Wing <7>s:

(7)R4C3=(7-8)R1C2=(8-5)R1C8=(5)R1C7-(5)R6C7=(5-3)R6C9=(3-7)R6C6=(7)R4C6; R4C1<>7

PS: I noticed the XYZ Wing but didn't want to post again until I found something more powerful. Don't know if I succeeded.
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Asellus



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

PostPosted: Thu Nov 15, 2007 10:44 am    Post subject: Reply with quote

Okay... another multi-coloring inspired AIC chips away at this beast:

(1)R8C5=(1-5)R8C9=(5)R6C9-(5=2)R6C7-(2=7)R6C1-(7=4)R8C1; R8C5<>4
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re'born



Joined: 28 Oct 2007
Posts: 80

PostPosted: Thu Nov 15, 2007 11:10 am    Post subject: Reply with quote

Asellus wrote:
Yeah... well while you were doing all that, I found a way to get rid of <7> in R4C1 by exploiting the strong inferential link between the W-Wing <7>s:

Asellus,
If I'm not mistaken, your AIC forms a loop, making all of the weak links strong and hence in addition to r4c1<>7, you also get r1c8<>7 and r9c7<>5.

Also, here is a way to kill 4 in r8c4 with just single digit coloring on the 4's:
(4):r8c1 = r2c1 - r3c3 = r3c7 - r1c7 = r1c4, => r8c4<>4.


Last edited by re'born on Thu Nov 15, 2007 12:04 pm; edited 1 time in total
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Asellus



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

PostPosted: Thu Nov 15, 2007 11:23 am    Post subject: Reply with quote

re'born wrote:
Asellus,
If I'm not mistaken, your AIC forms a loop, making all of the weak links strong and hence in addition to r4c1<>7, you also get r1c8<>7 and r9c7<>5.

Hmmm... I'll have to check that out later.

Meanwhile, I eliminated <4> in R2C1 (without your intervening R8C4 elimination) with a little group coloring (or ER):
(4)R8C1=(4)R8C4-(4)R12C4=(4)R2C6; R2C1<>4

It has nearly succumbed, and may have done so with the claimed loop eliminations.
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Asellus



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

PostPosted: Thu Nov 15, 2007 11:35 am    Post subject: Reply with quote

re'born,

That AIC loop makes sense to me. So, with the additional eliminations, this is the grid I now have:
Code:
+--------------+--------------+----------------+
| 9   78  6    | 47   3    1  | 457  58    2   |
| 78  12  5    | 2479 6    24 | 3    178   49  |
| 3   12  4    | 8    279  5  | 179  17    6   |
+--------------+--------------+----------------+
| 28  4   78   | 6    5    37 | 12   9     13  |
| 1   5   3    | 249  249  24 | 8    6     7   |
| 27  6   9    | 1    8    37 | 25   4     35  |
+--------------+--------------+----------------+
| 5   78  178  | 3    124  6  | 1479 127   49  |
| 4   9   2    | 57   17   8  | 6    3     15  |
| 6   3   17   | 245  124  9  | 147  1257  8   |
+--------------+--------------+----------------+

Now, I have to rest.
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re'born



Joined: 28 Oct 2007
Posts: 80

PostPosted: Thu Nov 15, 2007 11:55 am    Post subject: Reply with quote

An AIC finishes it from here:

(7=5)r8c4 - (5)r8c9 = (5)r6c9 - (5=2)r6c7 - (2=7)r6c1 - (7)r2c1 = (7)r1c2, => r1c4<>7, solving the puzzle.
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Asellus



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

PostPosted: Thu Nov 15, 2007 11:58 am    Post subject: Reply with quote

Okay... I didn't rest. I got the exact same AIC: it's a fairly straightforward Medusa trap.

[Edit: Not quite the same... my chain went via R6C6 rather than R6C7.]
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re'born



Joined: 28 Oct 2007
Posts: 80

PostPosted: Thu Nov 15, 2007 12:03 pm    Post subject: Reply with quote

Asellus wrote:
Okay... I didn't rest. I got the exact same AIC: it's a fairly straightforward Medusa trap.

[Edit: Not quite the same... my chain went via R6C6 rather than R6C7.]


Excellent! That was fun working it out together.
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Asellus



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

PostPosted: Thu Nov 15, 2007 8:58 pm    Post subject: Reply with quote

re'born wrote:
Excellent! That was fun working it out together.

Yes, and educational.

I realized this morning that that AIC loop would also eliminate <8> from R2C2 if the W-Wing structure is included in the loop (not just the pincers). It wouldn't have advanced the solution further that I can tell... though it would have tidied up the grid a bit more.
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