Help with the pattern

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Help with the pattern

Postby 813554 » Sat Sep 29, 2018 11:23 pm

Here's my puzzle: https://imgur.com/a/55Oa8Ad

As I did again, I saw that in b1, there's only 2 cells that can be 9. Then I've tried 9 for each of them, it showed me that r1c4 can not be 9. In the image, I've colored that. Now what is that pattern called? I don't want to do the same all the time, trying the numbers I mean. What is this pattern and how to detect it easier. I mean what to look to see that?
813554
 
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Joined: 05 September 2018

Re: Help with the pattern

Postby SpAce » Sun Sep 30, 2018 12:12 am

One way to describe it is an Empty Rectangle (here a special case with just two candidates in the hinge box), which is a kind of Turbot Fish. The other named Turbot Fishes are Skyscrapers and 2-String Kites. In general, Turbot Fishes are X-Chains of length 4, and X-Chains are single-digit AICs. In short, it's a chain which proves that at least one of its end nodes must be true. In this case it proves that either r1c2=9 or r4c4=9 (or both), and in neither case r1c4 can be 9. As a chain it's written:

(9)r1c2 = r2c1 - r4c1 = (9)r4c4 => -4 r1c4
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
SpAce
 
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Re: Help with the pattern

Postby 813554 » Sun Sep 30, 2018 10:22 am

Okay thanks. But as I said before, I look for a number which's 2 left in a box and 3 in other. This is how I detect it but it feels wrong. There must be an easier way, what should I look for to detect them?
813554
 
Posts: 13
Joined: 05 September 2018

Re: Help with the pattern

Postby SpAce » Sun Sep 30, 2018 6:27 pm

813554 wrote:Okay thanks. But as I said before, I look for a number which's 2 left in a box and 3 in other. This is how I detect it but it feels wrong. There must be an easier way, what should I look for to detect them?

I'm not sure what you're asking. You asked what the pattern you used was, and I told you. It was a common single-digit chaining pattern called Empty Rectangle or Turbot Fish. Probably the easiest way to find chains is exactly what you did: coloring. With experience you can learn to see some of them directly as patterns, too, so you don't necessarily need to follow the chaining logic. What you did, however, was exactly how and why the chain works, so nothing wrong with that. Can't help if it feels wrong to you.

One more time, here's your pattern:

Code: Select all
.----------------.---------------.--------------.
| 36  a8(9)* 36  | 1-9   149  7  | 2   5    48  |
|b89*  1     5   | 3     49   2  | 6   78   478 |
| 4    2     7   | 56    56   8  | 9   1    3   |
:----------------+---------------+--------------:
|c689* 7     1   |d8(9)* 2    36 | 38  4    5   |
| 389  4     389 | 589   59   1  | 7   2    6   |
| 2    5     68  | 4     7    36 | 38  9    1   |
:----------------+---------------+--------------:
| 17   36    2   | 16    8    5  | 4   37   9   |
| 17   36    4   | 2     16   9  | 5   378  78  |
| 5    89    89  | 7     3    4  | 1   6    2   |
'----------------'---------------'--------------'

Empty Rectangle/Turbot Fish: (9)r1c2 = r2c1 - r4c1 = (9)r4c4 => -9 r1c4

There's also another Empty Rectangle (of the more common type) in 9s that gives a different elimination:

Code: Select all
.----------------.----------------.--------------.
| 36   89  36    | 19   149    7  | 2   5    48  |
|c89*  1   5     | 3   d4(9)*  2  | 6   78   478 |
| 4    2   7     | 56   56     8  | 9   1    3   |
:----------------+----------------+--------------:
|b689* 7   1     | 89   2      36 | 38  4    5   |
|b389* 4  a38(9)*| 589  5-9    1  | 7   2    6   |
| 2    5   68    | 4    7      36 | 38  9    1   |
:----------------+----------------+--------------:
| 17   36  2     | 16   8      5  | 4   37   9   |
| 17   36  4     | 2    16     9  | 5   378  78  |
| 5    89  89    | 7    3      4  | 1   6    2   |
'----------------'----------------'--------------'

Empty Rectangle: (9)r5c3 = r45c1 - r2c1 = (9)r2c5 => -9 r5c5

There's also a Skyscraper in 9s which gives both of those eliminations at once:

Code: Select all
.--------------.------------------.--------------.
| 36   89  36  | 1-9    149    7  | 2   5    48  |
|b89*  1   5   | 3     a4(9)*  2  | 6   78   478 |
| 4    2   7   | 56     56     8  | 9   1    3   |
:--------------+------------------+--------------:
|c689* 7   1   |d8(9)*  2      36 | 38  4    5   |
| 389  4   389 | 589    5-9    1  | 7   2    6   |
| 2    5   68  | 4      7      36 | 38  9    1   |
:--------------+------------------+--------------:
| 17   36  2   | 16     8      5  | 4   37   9   |
| 17   36  4   | 2      16     9  | 5   378  78  |
| 5    89  89  | 7      3      4  | 1   6    2   |
'--------------'------------------'--------------'

Skyscraper: (9)r2c5 = r2c1 - r4c1 = (9)r4c4 => -9 r1c4, r5c5
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
SpAce
 
Posts: 504
Joined: 22 May 2017

Re: Help with the pattern

Postby 813554 » Sun Sep 30, 2018 7:58 pm

I mean, I can detect skyscrapers or X-wings more easily. When see 2 digits in a row or column with a strong link, I can see the the patterns but for this example, I have to follow the chain twice for each number (r1c2 and r2c1 in this case). In other examples it's enough to follow the chain once and I can eliminate some candidates. In this, I have to assume that r1c2 is 9, follow the chain, then I assume that r2c1 is 9 this time and follow the chain again. I mean, it doesn't feels right. But anyway, your reply really helped me, I saw it more clearly and I think I'll be able to see these patterns with less effort in time. Thank you.
813554
 
Posts: 13
Joined: 05 September 2018

Re: Help with the pattern

Postby SpAce » Sun Sep 30, 2018 10:18 pm

813554 wrote:I mean, I can detect skyscrapers or X-wings more easily. When see 2 digits in a row or column with a strong link, I can see the the patterns

X-Wings and Skyscrapers are easier to see exactly because both of their strong links are on either two rows or two columns. However, all the other X-Chains of length 4 have also two strong links (and one weak link), but they're just located differently:

X-Wing: both on rows or columns (weak links in opposite types of line)
Skyscraper: both on rows or columns (weak link in opposite type of line)
2-String Kite: one on a row, one on a column (weak link in a box)
Empty Rectangle: one on a row/column, one in a box (weak link on a row/column)

but for this example, I have to follow the chain twice for each number (r1c2 and r2c1 in this case). In other examples it's enough to follow the chain once and I can eliminate some candidates. In this, I have to assume that r1c2 is 9, follow the chain, then I assume that r2c1 is 9 this time and follow the chain again.

I don't quite understand. r1c2 sees the victim directly, so there's no chain needed for the case r1c2=9. You only need to follow the chain for the opposite case, i.e. if r1c2<>9 (-> r2c1=9). That's what the AIC depicts:

(9)r1c2 = r2c1 - r4c1 = (9)r4c4 => -9 r1c4

It can be read as follows: if r1c2=9 then r1c4<>4; else r2c1=9 -> r4c1<>9 -> r4c4=9 -> r1c4<>9. Thus, regardless of the truth value of r1c2, there can't be a 9 in r1c4. The chain works similarly the other way around too, i.e. if you start with r4c4. What it proves is that one or both of the chain ends must be a 9, and thus no cell weakly linked to both of them can't be a 9.

As a forcing chain (like you see it) it looks like:

(9)r1c2 - (9)r1c4
||
(9)r2c1 - r4c1 = r4c4 - (9)r1c4

=> -9 r1c4

But anyway, your reply really helped me, I saw it more clearly and I think I'll be able to see these patterns with less effort in time. Thank you.

You're welcome.
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
SpAce
 
Posts: 504
Joined: 22 May 2017

Re: Help with the pattern

Postby 813554 » Mon Oct 01, 2018 5:54 pm

When I first solved this, I couldn't see that strong link between r4c1 and r4c4. You're right, it makes this so much easier but let's assume that I couldn't eliminate 9 from the r4c7 cell. There's no longer a strong link between r4c1 and r4c4 but still it's possible to say r1c4 can't be 9, that was what I've colored. You can see I've used blue and green and each color represents one of my assumptions, that was why I had to follow the chain twice, I didn't see that strong link. Thank you again.
813554
 
Posts: 13
Joined: 05 September 2018

Re: Help with the pattern

Postby SpAce » Mon Oct 01, 2018 8:52 pm

813554 wrote:When I first solved this, I couldn't see that strong link between r4c1 and r4c4. You're right, it makes this so much easier but let's assume that I couldn't eliminate 9 from the r4c7 cell. There's no longer a strong link between r4c1 and r4c4 but still it's possible to say r1c4 can't be 9, that was what I've colored. You can see I've used blue and green and each color represents one of my assumptions, that was why I had to follow the chain twice, I didn't see that strong link. Thank you again.

I still don't see what you mean by following the chain twice. Even if you use the longer grouped chain (which is a valid, though unnecessarily complicated, option) the logic is the same:

(9)r1c2 = r2c1 - r45c1 = r5c3 - r5c45 = (9)r4c4 => -9 -r1c4

Again, either r1c2=9 (-> r1c4<>9) or r2c1=9 (->...-> r4c4=9 -> r1c4<>9). Only the latter case requires following a chain as r1c2 sees the victim directly.
SpAce
 
Posts: 504
Joined: 22 May 2017


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