Which adv technique do I apply here?

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Which adv technique do I apply here?

Postby mameshiba » Sun Oct 22, 2017 12:59 pm

My first post :)
I have loved solving sudoku puzzles for ages but it wasn't until recently that I found out about advanced solving techniques. The hidden pairs and hidden triples have been natural techniques to me.

Here's a puzzle I'm doing right now:
Image

This is where I'm stuck. I've stared at it for long and knowing what I know won't get me further. I always get to this point where there's a 50-50 chance. I want to keep eliminating. :o

Which technique would you apply next??

Does this x-wing work to eliminate 4 in r5c2 and r5c3?
Image
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Re: Which adv technique do I apply here?

Postby JC Van Hay » Sun Oct 22, 2017 10:59 pm

Code: Select all
+---------------+-------------+-----------+
| 134  146  2   | 146  8   13 | 7   5  9  |
| 8    5    16  | 16   9   7  | 3   4  2  |
| 347  47   9   | 24   5   23 | 6   1  8  |
+---------------+-------------+-----------+
| 9    8    7   | 3    12  4  | 25  6  15 |
| 245  246  456 | 7    12  9  | 8   3  14 |
| 124  3    14  | 8    6   5  | 24  9  7  |
+---------------+-------------+-----------+
| 6    14   145 | 9    7   8  | 45  2  3  |
| 245  9    8   | 25   3   6  | 1   7  45 |
| 257  27   3   | 125  4   12 | 9   8  6  |
+---------------+-------------+-----------+
1. 4r6c1 is excluded by the solutions of the digit 4.
Code: Select all
+----------------------+---------------+---------------+
| 13(4)   16(4)  2     | 16(4)  8   13 | 7     5  9    |
| 8       5      16    | 16     9   7  | 3     4  2    |
| 37(4)   7(4)   9     | 2(4)   5   23 | 6     1  8    |
+----------------------+---------------+---------------+
| 9       8      7     | 3      12  4  | 25    6  15   |
| 25(4)   26(4)  56(4) | 7      12  9  | 8     3  1(4) |
| 12(-4)  3      1(4)  | 8      6   5  | 2(4)  9  7    |
+----------------------+---------------+---------------+
| 6       1(4)   15(4) | 9      7   8  | 5(4)  2  3    |
| 25(4)   9      8     | 25     3   6  | 1     7  5(4) |
| 257     27     3     | 125    4   12 | 9     8  6    |
+----------------------+---------------+---------------+
Interpretations : the solutions of XWing(4R48) or Kite(4R8C7) or ER(4C7B7) exclude 4r6c1

2. Observations :
2a. C6 has only 2 solutions
2b. B569 has only 2 solutions

3. The 2 solutions of B569 imply r8c4=2 and 9 singles solving C6R39B8.
Code: Select all
+-----------------+---------------+---------------+
| 134    146  2   | 146    8   13 | 7     5  9    |
| 8      5    16  | 16     9   7  | 3     4  2    |
| 347    47   9   | 24     5   23 | 6     1  8    |
+-----------------+---------------+---------------+
| 9      8    7   | 3      12  4  | (25)  6  1(5) |
| 245    246  456 | 7      12  9  | 8     3  14   |
| 1(2)   3    14  | 8      6   5  | 4(2)  9  7    |
+-----------------+---------------+---------------+
| 6      14   145 | 9      7   8  | 45    2  3    |
| 45(2)  9    8   | -5(2)  3   6  | 1     7  4(5) |
| 257    27   3   | 125    4   12 | 9     8  6    |
+-----------------+---------------+---------------+
An interpretation : r4c7=r6c1=r8c4=2 or r4c7=r8c9=5, r8c4=2
Eureka notation : 2r8c4=2r8c1-2r6c1=2r6c7-(2=5)r4c7-5r4c9=5r8c9 -> derived constraint {2r8c4, 5r8c9} => -5r8c4; 10 singles

4. One of the solution of B569 exclude 5C1
Code: Select all
+-----------------+-----------+----------------+
| 14     146  2   | 16  8   3 | 7      5  9    |
| 8      5    16  | 16  9   7 | 3      4  2    |
| 3      7    9   | 4   5   2 | 6      1  8    |
+-----------------+-----------+----------------+
| 9      8    7   | 3   12  4 | -5(2)  6  1(5) |
| 4(25)  46   456 | 7   12  9 | 8      3  14   |
| 1(2)   3    14  | 8   6   5 | 4(2)   9  7    |
+-----------------+-----------+----------------+
| 6      14   145 | 9   7   8 | 45     2  3    |
| 4(5)   9    8   | 2   3   6 | 1      7  4(5) |
| 7      2    3   | 5   4   1 | 9      8  6    |
+-----------------+-----------+----------------+
An interpretation : r4c7=5 -> r8c9=5 and r6c7=r5c1=2; 5C1={} => r4c7=2 and singles to the end.
Eureka notation : 2r4c7=2r6c7-2r6c1=(2-5)r5c1=5r8c1-5r8c9=5r4c9 -> derived constraint {2r4c7, 5r4c9} => -5r4c7; stte
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Re: Which adv technique do I apply here?

Postby SteveG48 » Sun Oct 22, 2017 11:15 pm

mameshiba wrote:My first post :)


Welcome aboard!

Does this x-wing work to eliminate 4 in r5c2 and r5c3?
Image


No, it doesn't, because you have 4's in r1c1, r3c1, and r6c1.

As JC points out, you can eliminate the 4 in r6c1 using several techniques, including a kite and a finned x-wing. The kite seems most appropriate here. It's at r67c7 and r8c19. After that, you want to read up on XY-wings and W-wings, but be warned, you have a few steps to go. It's not a trivial puzzle if you're just starting with advanced techniques.
Steve
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Re: Which adv technique do I apply here?

Postby Leren » Sun Oct 22, 2017 11:51 pm

The puzzle solved cell status in line format : ..2.8.75985..97342..9.5.6189873.4.6....7.983..3.865.976..978.23.98.3617...3.4.986

To answer your X Wing question first, there is no ordinary X Wing where you say, but there is a related chain involving digit 4 that makes one elimination.

Code: Select all
*---------------------------------------*
| 134   146  2   | 146 8  13 | 7  5  9  |
| 8     5    16  | 16  9  7  | 3  4  2  |
| 347   47   9   | 24  5  23 | 6  1  8  |
|----------------+-----------+----------|
| 9     8    7   | 3   12 4  | 25 6  15 |
|d245  d246 d456 | 7   12 9  | 8  3 c14 |
| 12-4  3    14  | 8   6  5  | 24 9  7  |
|----------------+-----------+----------|
| 6     14   145 | 9   7  8  | 45 2  3  |
|a245   9    8   | 25  3  6  | 1  7 b45 |
| 257   27   3   | 125 4  12 | 9  8  6  |
*---------------------------------------*

If Cell a is not 4, Cell b must be 4, so Cell c is not 4, so one of the three Cells marked d must be 4.

Since r6c1 can see all of Cells a and d, at least one of which must be True, it can't be 4 and can be eliminated.

This move can be described in two ways, a Grouped Skyscraper or a Finned X Wing. The Finned XWing is in Rows 58 Columns 19 and has 2 fin cells in r5c23.

Only the X Wing eliminations in Columns 18 that can see the fin cells can be eliminated, so you only get one. Unfortunately this move doesn't really help all that much, so I'll give you a two move solution instead.

Code: Select all
*-------------------------------------*
| 134  146 2   | 146 8  13 | 7  5  9  |
| 8    5   16  | 16  9  7  | 3  4  2  |
| 347  47  9   | 24  5  23 | 6  1  8  |
|--------------+-----------+----------|
| 9    8   7   | 3   12 4  |d25 6 e15 |
| 245  246 456 | 7   12 9  | 8  3  14 |
|a12-4 3   14  | 8   6  5  |b24 9  7  |
|--------------+-----------+----------|
| 6    14  145 | 9   7  8  | 45 2  3  |
|g45-2 9   8   | 25  3  6  | 1  7 f45 |
| 257  27  3   | 125 4  12 | 9  8  6  |
*-------------------------------------*

There is an Alternating Inference Chain AIC in cells a-b-c-d-e-f-g for which the Eureka notation is (2) r6c1 = r6c7 - (2=5) r4c7 - r4c9 = (5-4) r8c9 = (4) r8c1

What this says is that if you assume Cell a is not 2, Cell g is 4. Conversely if you start by assuming Cell g is not 4, then Cell a is 2. This => Cell a is not 4 and Cell g is not 2.

With some subsequent singles this eventually gets you to here.

Code: Select all
*------------------------------------*
| 14  146 2   | 16  8   3 | 7  5  9  |
| 8   5   16  | 16  9   7 | 3  4  2  |
| 3   7   9   | 4   5   2 | 6  1  8  |
|-------------+-----------+----------|
| 9   8   7   | 3  a1-2 4 | 25 6 b15 |
|e245 46  456 | 7  f2-1 9 | 8  3  14 |
| 12  3   14  | 8   6   5 | 24 9  7  |
|-------------+-----------+----------|
| 6   14  145 | 9   7   8 | 45 2  3  |
|d45  9   8   | 2   3   6 | 1  7 c45 |
| 7   2   3   | 5   4   1 | 9  8  6  |
*------------------------------------*

Similarly to the first move there is an AIC in Cells a-b-c-d-e-f for which the Eureka notation is (1) r4c5 = (1-5) r4c9 = r8c9 - r8c1 = (5-2) r5c1 = (2) r5c5. This => Cell a is not 2 and Cells f is not 1.

The puzzle solves in singles from there. Sorry about the complex moves but this puzzle was surprisingly resistant so close to the end.

If you want to understand more about AIC's you can read about them here. I can also provide links to write-ups on finned X Wings and Skyscrapers if you want.

Leren
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