June 28, 2020

Post puzzles for others to solve here.

June 28, 2020

Postby tarek » Sun Jun 28, 2020 7:32 am

Code: Select all
+-------+-------+-------+
| . 7 . | . 3 1 | 4 . . |
| 1 . . | 5 . . | . 6 2 |
| . . 6 | . 8 2 | . 7 . |
+-------+-------+-------+
| . 2 . | . . . | . . . |
| 8 . 9 | . . 4 | 5 . . |
| 3 . 4 | . 5 8 | . . . |
+-------+-------+-------+
| 2 . . | . 7 . | . . . |
| . 9 5 | . . . | . . 1 |
| . 8 . | . . . | . 5 . |
+-------+-------+-------+
.7..314..1..5...62..6.82.7..2.......8.9..45..3.4.58...2...7.....95.....1.8.....5.

Play this puzzle online

Download Sukaku Explainer
User avatar
tarek
 
Posts: 3762
Joined: 05 January 2006

Re: June 28, 2020

Postby Leren » Sun Jun 28, 2020 8:56 am

Code: Select all
*---------------------------------------------*
| 9   7  2  | 6     3    1   | 4    8     5   |
| 1   3  8  | 5     4    7   | 9    6     2   |
| 4   5  6  | 9     8    2   | 1    7     3   |
|-----------+----------------+----------------|
| 5   2  7  |b13    169  369 | 368  134   468 |
| 8  a16 9  |b1237 a126  4   | 5    123 ca67  |
| 3   16 4  |b127   5    8   | 26-7 129  c679 |
|-----------+----------------+----------------|
| 2   4  13 |b138   7    5   | 368  39   c689 |
| 67  9  5  | 2348  26   36  | 2378 234   1   |
| 67  8  13 | 1234  1269 369 | 237  5     4-7 |
*---------------------------------------------*

(7=2) r5c259 - (2=8) r4567c4 - (8=7) r567c9 => - 7 r6c7; r9c9; stte

Leren
Leren
 
Posts: 5019
Joined: 03 June 2012

Re: June 28, 2020

Postby SpAce » Sun Jun 28, 2020 10:35 am

Code: Select all
.------------.-------------------.-------------------.
| 9   7   2  |  6      3     1   |  4     8      5   |
| 1   3   8  |  5      4     7   |  9     6      2   |
| 4   5   6  |  9      8     2   |  1     7      3   |
:------------+-------------------+-------------------:
| 5   2   7  |  13     169   369 | f368   134   g468 |
| 8   16  9  | b1237  c126   4   |  5    c123   a67  |
| 3   16  4  | d127    5     8   |  267   129    679 |
:------------+-------------------+-------------------:
| 2   4   13 |  138    7     5   |  368   39     689 |
| 67  9   5  | e2348   26    36  | e2378  234    1   |
| 67  8   13 | b1234   1269  369 |  237   5    ag4-7 |
'------------'-------------------'-------------------'

(7)r5c9|(4)r9c9 = (74-3|2)r59c4 = [(+32)r5c85 - r6c4 = (2,8)r8c47 - r4c7 = (84)r49c9] => -7 r9c9; stte

as a Kraken Column 2C4: Show
Code: Select all
(2-7)r5c4 = (7)r5c9
||
(2)r6c4 - r5c45 = (2-3)r5c8 = (3-7)r5c4 = (7)r5c9
||
(2-8)r8c4 = r8c7 - r4c7 = (8-4)r4c9 = (4)r9c9
||
(2-4)r9c4 = (4)r9c9

=> -7 r9c9; stte

8x8 PM: Show
Code: Select all
 4r9c9 4r4c9
       8r4c9 8r4c7
             8r8c7 8r8c4
 4r9c9 ................. 4r9c4
 7r5c9 ....................... 7r5c4
                   2r8c4 2r9c4 2r5c4 2r6c4
                                     2r5c45 2r5c8
                               3r5c4 ...... 3r5c8
=================================================
-7r9c9

Btw, appearances can deceive. While this is obviously way uglier and more complicated as an AIC than Leren's neat and elegant ALS-XY-Wing, which one is really more complicated? It's hard to say, because it depends on several factors, and I make no claims either way. (I think I'm leaning on Leren's, though. Edit: I actually meant I was leaning on Leren's being simpler, all things considered.) What is certain, however, is that as a matrix the ALS-XY-Wing doesn't look so simple any more:

9x9 BTM (Leren): Show
Code: Select all
 7r5c9 6r5c9
       6r5c2 1r5c2
       6r5c5 1r5c5 2r5c5
                   2r6c4 1r6c4 7r6c4
                   2r5c4 1r5c4 7r5c4 3r5c4
                         1r4c4 ..... 3r4c4
                         1r7c4 ..... 3r7c4 8r7c4
       6r7c9                               8r7c9 9r7c9
 7r6c9 6r6c9 ................................... 9r6c9
======================================================
-7r9c9
Last edited by SpAce on Sun Jun 28, 2020 11:51 am, edited 2 times in total.
-SpAce-: Show
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."
User avatar
SpAce
 
Posts: 2671
Joined: 22 May 2017

Re: June 28, 2020

Postby Cenoman » Sun Jun 28, 2020 11:36 am

Code: Select all
 +-----------------+----------------------+---------------------+
 |  9    7    2    |  6      3      1     |  4      8     5     |
 |  1    3    8    |  5      4      7     |  9      6     2     |
 |  4    5    6    |  9      8      2     |  1      7     3     |
 +-----------------+----------------------+---------------------+
 |  5    2    7    |  13     169    369   | a36-8*  134  b468*  |
 |  8   d16   9    |  1237  d126    4     |  5      123  c67    |
 |  3    16   4    |  127    5      8     |  267    129   679   |
 +-----------------+----------------------+---------------------+
 |  2    4    13   |  138    7      5     |  368*   39    689*  |
 |  67   9    5    | f2348  e26     36    |ga2378   234   1     |
 |  67   8    13   | f1234  e1269   369   |  237    5    c47    |
 +-----------------+----------------------+---------------------+

UR(68)r47c79 using mixed internals-external
(3)r4c7|(8)r8c7 == (4)r4c9 - (4=76)r59c9 - (6=12)r5c25 - r89c5 = (24-8)r89c4 = (8)r8c7 => -8 r4c7; ste
Cenoman
Cenoman
 
Posts: 2710
Joined: 21 November 2016
Location: France

Re: June 28, 2020

Postby SteveG48 » Sun Jun 28, 2020 3:53 pm

Code: Select all
 *------------------------------------------------------------*
 | 9     7     2     |  6     3     1     | 4     8     5     |
 | 1     3     8     |  5     4     7     | 9     6     2     |
 | 4     5     6     |  9     8     2     | 1     7     3     |
 *-------------------+--------------------+-------------------|
 | 5     2     7     | c13    169   369   | 368   134   468   |
 | 8    a16    9     |bc1237 a126   4     | 5    a123   7-6   |
 | 3     16    4     |bc127   5     8     | 267   129   679   |
 *-------------------+--------------------+-------------------|
 | 2     4     13    | c138   7     5     | 368 bc39   d689   |
 | 67    9     5     |  2348  26    36    | 2378  234   1     |
 | 67    8     13    |  1234  1269  369   | 237   5     47    |
 *------------------------------------------------------------*


(6=123)r5c258 - 2r56c4|3r7c8 = (13789)r4567c4,r7c8 - (8|9=6)r7c9 => -6 r5c9 ; stte

Yarg. Practically the same as Leren's but not nearly as nice.
Steve
User avatar
SteveG48
2019 Supporter
 
Posts: 4202
Joined: 08 November 2013
Location: Orlando, Florida

Re: June 28, 2020

Postby SpAce » Mon Jun 29, 2020 4:01 am

Hi Steve,

SteveG48 wrote:(6=123)r5c258 - 2r56c4|3r7c8 = (13789)r4567c4,r7c8 - (8|9=6)r7c9 => -6 r5c9 ; stte

Yarg. Practically the same as Leren's but not nearly as nice.

I think it's different enough, and niceness is somewhat subjective. Personally I hate ALS terms without the passenger digits (hard to read against the grid, looks simpler than it really is), so everything is nicer than that :) Disregarding that easily fixed style issue we can of course agree that Leren's AIC is the cleanest. However, the (unfolded) matrix of yours is actually a bit nicer because it can be written as a TM:

9x9 TM: Show
Code: Select all
 6r5c2 1r5c2
 6r5c5 1r5c5 2r5c5
       1r5c8 2r5c8 3r5c8
       1r5c4 2r5c4 3r5c4 7r5c4
             2r6c4 ..... 7r6c4 1r6c4
                               1r4c4 3r4c4
                               1r7c4 3r7c4 8r7c4
                   3r7c8 ....................... 9r7c8
 6r7c9 ................................... 8r7c9 9r7c9
======================================================
-6r5c9

That's slightly different from your AIC, corresponding with:

(6=123)r5c258 - (2|3)r56c4,r7c8 ...

As for the following term, I might consider using an optional comma to (subjectively) improve readability:

(7138,9)r6547c4,r7c8

or perhaps:

(713,89)r654c4,r7c48 - (8|9=6)r7c9

The latter form makes the following weak link easier to read, but it kind of blurs the reason for 8r7c4, so neither is perfect. This might be stretching a bit too much, though it would give a pretty short AIC:

(6=123)r5c258 - (2|3)r56c4,r7c8 = (713,896)r654c4,r7c489 => -6 r5c9 ; stte

(This is pure speculation of possibilities. Nothing wrong with your original!)

From a resource management perspective, yours and Leren's are similar. Both use 9 cells, 7 digits, and 25 candidates. Mine uses 11 cells, 5 digits, and 17 candidates. That's what I meant earlier about the difficulty of judging complexity. For that I mostly look at the unfolded matrix form, though it doesn't necessarily tell the whole story either.
User avatar
SpAce
 
Posts: 2671
Joined: 22 May 2017


Return to Puzzles