Tough nut to crack?

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Tough nut to crack?

Postby Draco » Sat May 10, 2008 9:04 pm

Seems like a slow Saturday, so here's a 23-spot puzzle to mull:
Code: Select all
7 . . | . . 2 | . . .
. . . | . . . | . . 4
. 9 . | . 7 . | 6 . 1
------+-------+------
3 . 4 | . . . | 5 2 .
. . . | . 1 . | . . .
. 5 8 | . . . | 4 . 7
------+-------+------
1 . 7 | . 3 . | . 9 .
8 . . | . . . | . . .
. . . | 6 . . | . . 3


After SSTS you'll find:
Code: Select all
7  368 1356 | 13458  456 2     | 39 358 589
56 38  135  | 13589  59  13689 | 2  7   4 
4  9   2    | 358    7   38    | 6  358 1 
------------+------------------+-----------
3  1   4    | 78     69  78    | 5  2   69
2  7   69   | 45     1   45    | 39 368 689
69 5   8    | 39     2   369   | 4  1   7 
------------+------------------+-----------
1  46  7    | 245    3   45    | 8  9   256
8  346 36   | 124579 459 179   | 17 56  256
59 2   59   | 6      8   17    | 17 4   3 


I've found a single, short forcing chain that cracks it to SSTS to solve using the coloring on 4's for my bi-value:

r1c4=4 r1c3=1 + r1c5=4 r2c6=6 r2c1=5 ==> r1c3<>5.

Looking for interesting alternatives.

Cheers...

- drac

[edit: oops on acronyms corrected]
[edit: pasted correct PM's into msg - thanks RW!]
Last edited by Draco on Sat May 10, 2008 7:23 pm, edited 1 time in total.
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Re: Tough nut to crack?

Postby RW » Sat May 10, 2008 10:52 pm

Draco wrote:After SSTS you'll find:
Code: Select all
7  368 1356 | 134589 4569 2      | 39 358 589
56 368 1356 | 13589  569  135689 | 2  7   4 
4  9   2    | 358    7    358    | 6  358 1 
------------+--------------------+-----------
3  1   4    | 789    69   6789   | 5  2   689
2  7   69   | 34589  1    345689 | 39 368 689
69 5   8    | 39     2    369    | 4  1   7 
------------+--------------------+-----------
1  46  7    | 245    3    45     | 8  9   256
8  346 3569 | 124579 459  14579  | 17 56  256
59 2   59   | 6      8    1579   | 17 4   3 

:?::?:
After SSTS I find:
Code: Select all
 *-----------------------------------------------------------------------------*
 | 7       368     1356    | 13458   456     2       | 39      358     589     |
 | 56      38      135     | 13589   59      13689   | 2       7       4       |
 | 4       9       2       | 358     7       38      | 6       358     1       |
 |-------------------------+-------------------------+-------------------------|
 | 3       1       4       | 78      69      78      | 5       2       69      |
 | 2       7       69      | 45      1       45      | 39      368     689     |
 | 69      5       8       | 39      2       369     | 4       1       7       |
 |-------------------------+-------------------------+-------------------------|
 | 1       46      7       | 245     3       45      | 8       9       256     |
 | 8       346     36      | 124579  459     179     | 17      56      256     |
 | 59      2       59      | 6       8       17      | 17      4       3       |
 *-----------------------------------------------------------------------------*

One of the two type 1 URs will crack it (together with SSTS).

RW
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Postby Draco » Sat May 10, 2008 11:25 pm

Oops... pasted the wrong PM's the first time; thanks RW. I've corrected the original post.

I'm not seeing the UR's (and am also bad at spotting them); would you mind calling them out more specifically? Thx!

- drac
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Postby Glyn » Sat May 10, 2008 11:50 pm

Draco here's two UR's

1)r57c46 => r7c4=2 to avoid {45}
2)r89c67 => r8c6=9 to avoid {17}
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Postby Draco » Sun May 11, 2008 1:27 am

Sigh -- thanks Glyn.
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Postby Jean-Christophe » Sun May 11, 2008 9:22 am

If you don't want using uniqueness techniques, here is an alternative:

Sashimi Swordfish on 5 in r357 and c468 with fin in r7c9 -> r8c8 <> 5 = 6
or
Grouped 2 String Kite (5): r3c8=r3c4-r12c5=r8c5 -> r8c8 <> 5 = 6
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Postby Carcul » Sun May 11, 2008 11:37 am

Code: Select all
 *--------------------------------------------------------------------*
 | 7       3468    1356 | 13458   456     2     | 39      358     589 |
 | 56      368     1356 | 13589   569     13689 | 2       7       4   |
 | 245     9       235  | 3458    7       38    | 6       358     1   |
 |----------------------+-----------------------+---------------------|
 | 3       1       4    | 78      69      78    | 5       2       69  |
 | 269     7       269  | 45      1       45    | 39      368     689 |
 | 69      5       8    | 239     269     369   | 4       1       7   |
 |----------------------+-----------------------+---------------------|
 | 1       46      7    | 245     3       45    | 8       9       256 |
 | 8       346     356  | 124579  2459    179   | 17      456     256 |
 | 459     2       59   | 6       8       17    | 17      45      3   |
 *--------------------------------------------------------------------*

[r7c2]=6=[r7c9]-6-[r89c8]-5-[r3c68]-3,8-[r35c4]-4-[r18c4]=4=[r8c2]-4-[r7c2], => r7c2<>4 and the puzzle is solved.
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Postby ronk » Sun May 11, 2008 2:44 pm

Carcul wrote:
Code: Select all
 *----------------------------------------------------------*
 | 7     3468  1356 | 13458   456   2     | 39    358   589 |
 | 56    368   1356 | 13589   569   13689 | 2     7     4   |
 | 245   9     235  | 3458    7     38    | 6     358   1   |
 |------------------+---------------------+-----------------|
 | 3     1     4    | 78      69    78    | 5     2     69  |
 | 269   7     269  | 45      1     45    | 39    368   689 |
 | 69    5     8    | 239     269   369   | 4     1     7   |
 |------------------+---------------------+-----------------|
 | 1     46    7    | 245     3     45    | 8     9     256 |
 | 8     346   356  | 124579  2459  179   | 17    456   256 |
 | 459   2     59   | 6       8     17    | 17    45    3   |
 *----------------------------------------------------------*

[r7c2]=6=[r7c9]-6-[r89c8]-5-[r3c68]-3,8-[r35c4]-4-[r18c4]=4=[r8c2]-4-[r7c2], => r7c2<>4 and the puzzle is solved.

All I see one of Mike Barker's kraken x-wings, but the notation sure doesn't say that. However, if that is the technique you're using, it's one of the few cases where I prefer AIC notation over NL notation.

Code: Select all
(4)x-wing:r18\c25
    ||
(4)fin:r8c8 - (4)r9c8 = (4)r9c1
    ||
(4)fin:r18c4 - (4=38)r35c4 - (38=5)r3c68 - (5=46)r89c8 - (6)r7c9 =(6)r7c2 ==> r7c2<>4
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Postby Carcul » Mon May 12, 2008 10:12 pm

No, that's not the technique I used. Where are your doubts (if any)?
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Postby Draco » Mon May 12, 2008 10:53 pm

Jean-Christophe wrote:If you don't want using uniqueness techniques, here is an alternative:

Sashimi Swordfish on 5 in r357 and c468 with fin in r7c9 -> r8c8 <> 5 = 6
or
Grouped 2 String Kite (5): r3c8=r3c4-r12c5=r8c5 -> r8c8 <> 5 = 6

Thanks Jean... it's not that I don't like UR's. It's that I cannot believe how blind I am when it comes to spotting them!:(
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Postby Draco » Mon May 12, 2008 11:04 pm

Carcul wrote:[r7c2]=6=[r7c9]-6-[r89c8]-5-[r3c68]-3,8-[r35c4]-4-[r18c4]=4=[r8c2]-4-[r7c2], => r7c2<>4 and the puzzle is solved.

That is one heckuva' chain! Compared to using ALS's in a chain, I find UR's easy:) .

I am able to follow it (I think) up to ... "[r18c4]=4=[r8c2]". Why is r8c2 set to 4? Isn't r8c8=4 also valid from the posted PMs and your chain up to that point? What am I missing?

Cheers...

- drac
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Postby ronk » Tue May 13, 2008 12:27 am

Carcul wrote:No, that's not the technique I used. Where are your doubts (if any)?

Instead of playing Mr. Cutesy, why don't you explain your derived strong inference?

[edit: Don't explain on my account though, as I've lost interest.]
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Postby daj95376 » Tue May 13, 2008 8:14 am

If you perform Colors on 4 after [r18c4]=4=, then you get [r8c5] and [r8c8] as the same color. This forces =4=[r8c2].

Thus, Carcul's [r18c4]=4=[r8c2].
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Postby Draco » Wed May 14, 2008 3:29 am

daj95376 wrote:If you perform Colors on 4 after [r18c4]=4=, then you get [r8c5] and [r8c8] as the same color. This forces =4=[r8c2].

Thus, Carcul's [r18c4]=4=[r8c2].

Ah, ok. I was trying with a static grid. Thx...

- drac
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