A Loopy Puzzle

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A Loopy Puzzle

Postby Yogi » Mon Dec 14, 2020 3:48 am

107020300632701450005600172308207510710000823520010907261004705073152680850076201

Loop.png
Loop.png (51.16 KiB) Viewed 57 times

The candidate box analysis here indicates that single-digit eliminations may be found in only two candidates, and it turns out that there are quite a few conjugate pairs for them: 4r1689c1489 & 9r248c13. Interestingly, for all that I found only one X Wing elimination: r5c3 <>4 which didn’t lead to much.
However, I recall someone mentioning that when you see lots of CPs the situation is ripe for finding Loops, which can generate more eliminations than single-digit techniques. But where are they?
Yogi
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Re: A Loopy Puzzle

Postby denis_berthier » Mon Dec 14, 2020 4:29 am

Yogi wrote:107020300632701450005600172308207510710000823520010907261004705073152680850076201
Loop.png

The candidate box analysis here indicates that single-digit eliminations may be found in only two candidates, and it turns out that there are quite a few conjugate pairs for them: 4r1689c1489 & 9r248c13. Interestingly, for all that I found only one X Wing elimination: r5c3 <>4 which didn’t lead to much.
However, I recall someone mentioning that when you see lots of CPs the situation is ripe for finding Loops, which can generate more eliminations than single-digit techniques. But where are they?


Not sure what you're asking for, but you can get a solution with bivalue-chains only (and even with typed ones only):
(Notice that Pairs are particular bivalue-chains.

Hidden Text: Show
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = TyBC
*** Using CLIPS 6.32-r773
***********************************************************************************************
77 candidates, 276 csp-links and 276 links. Density = 9.43%
naked-pairs-in-a-row: r6{c3 c8}{n4 n6} ==> r6c4 ≠ 4
hidden-pairs-in-a-column: c4{n4 n5}{r1 r5} ==> r5c4 ≠ 9, r1c4 ≠ 9, r1c4 ≠ 8
whip[1]: c4n9{r9 .} ==> r7c5 ≠ 9
biv-chain-rn[2]: r9n4{c3 c8} - r6n4{c8 c3} ==> r5c3 ≠ 4
whip[1]: r5n4{c5 .} ==> r4c5 ≠ 4
biv-chain-cn[4]: c3n6{r5 r6} - c3n4{r6 r9} - c1n4{r8 r3} - c5n4{r3 r5} ==> r5c5 ≠ 6
stte
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Re: A Loopy Puzzle

Postby Leren » Mon Dec 14, 2020 5:09 am

Code: Select all
*-------------------------------------------*
| 1  489 7   | 45   2     589 | 3  69   689 |
| 6  3   2   | 7    89    1   | 4  5    89  |
|a49 489 5   | 6   f389-4 389 | 1  7    2   |
|------------+----------------+-------------|
| 3  49  8   | 2    469   7   | 5  1    46  |
| 7  1   469 | 45   469   59  | 8  2    3   |
| 5  2   46  | 38   1     38  | 9  46   7   |
|------------+----------------+-------------|
| 2  6   1   | 389 e38    4   | 7 d39   5   |
|b49 7   3   | 1    5     2   | 6  8   c49  |
| 8  5   49  | 39   7     6   | 2  349  1   |
*-------------------------------------------*

(4) r3c1 = (4-9) r8c1 = r8c9 - (9=3) r7c8 - r7c5 = (3) r3c5 => - 4 r3c5; stte

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Re: A Loopy Puzzle

Postby Leren » Mon Dec 14, 2020 5:25 am

Code: Select all
*------------------------------------------*
| 1  489  7    | 45  2    589 | 3  69  689 |
| 6  3    2    | 7   89   1   | 4  5   89  |
| 49 489  5    | 6   3489 389 | 1  7   2   |
|--------------+--------------+------------|
| 3  49   8    | 2   469  7   | 5  1   46  |
| 7  1    69-4 | 45  469  59  | 8  2   3   |
| 5  2   *46   | 38  1    38  | 9 *46  7   |
|--------------+--------------+------------|
| 2  6    1    | 389 38   4   | 7  39  5   |
| 49 7    3    | 1   5    2   | 6  8   49  |
| 8  5   *49   | 39  7    6   | 2 *349 1   |
*------------------------------------------*

A humble X Wing is a loop. Later on I found :

Code: Select all
*-------------------------------------------*
| 1  f489 7  | 45   2     589 | 3 69   68-9 |
| 6   3   2  | 7   a89    1   | 4 5   b89   |
|e49 f489 5  | 6    348-9 389 | 1 7    2    |
|------------+----------------+-------------|
| 3  g49  8  | 2   h69    7   | 5 1    46   |
| 7   1   69 | 45   46-9  59  | 8 2    3    |
| 5   2   46 | 38   1     38  | 9 46   7    |
|------------+----------------+-------------|
| 2   6   1  | 389  38    4   | 7 39   5    |
|d49  7   3  | 1    5     2   | 6 8   c49   |
| 8   5   49 | 39   7     6   | 2 349  1    |
*-------------------------------------------*

X Chain Continuous Loop: (9) r2c5 = r2c9 - r8c9 = r8c1 - r3c1 = r13c2 - r4c2 = r4c5 => - 9 r1c9, r35c5

But that still doesn't solve the puzzle. For stte-aholics like me it's often a good idea to ignore continuous loops because, even though they look cool and have several eliminations, they often don't solve a cell, so you don't get your stte hit.

Leren
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Re: A Loopy Puzzle

Postby RSW » Mon Dec 14, 2020 10:10 am

An X-wing, 3 X-Chains and one XY-Chain.
Hidden Text: Show
Code: Select all
 +------------+--------------+-----------+
 | 1  489 7   | 45  2    589 | 3 69  689 |
 | 6  3   2   | 7   89   1   | 4 5   89  |
 | 49 489 5   | 6   3489 389 | 1 7   2   |
 +------------+--------------+-----------+
 | 3  49  8   | 2   469  7   | 5 1   46  |
 | 7  1   469 | 45  469  59  | 8 2   3   |
 | 5  2   46  | 38  1    38  | 9 46  7   |
 +------------+--------------+-----------+
 | 2  6   1   | 389 38   4   | 7 39  5   |
 | 49 7   3   | 1   5    2   | 6 8   49  |
 | 8  5   49  | 39  7    6   | 2 349 1   |
 +------------+--------------+-----------+

2-Fish (aka X-Wing): In rows 6 9, digit 4 must go in columns 3 8 => -4r5c3.
Code: Select all
 +-----------+--------------+-----------+
 | 1  489 7  | 45  2    589 | 3 69  689 |
 | 6  3   2  | 7   89   1   | 4 5   89  |
 | 49 489 5  | 6   3489 389 | 1 7   2   |
 +-----------+--------------+-----------+
 | 3  49  8  | 2   69   7   | 5 1   46  |
 | 7  1   69 | 45  469  59  | 8 2   3   |
 | 5  2   46 | 38  1    38  | 9 46  7   |
 +-----------+--------------+-----------+
 | 2  6   1  | 389 38   4   | 7 39  5   |
 | 49 7   3  | 1   5    2   | 6 8   49  |
 | 8  5   49 | 39  7    6   | 2 349 1   |
 +-----------+--------------+-----------+

X-chain: (9)r2c5=r2c9-r8c9=r8c1-r9c3=r5c3 => -9r5c5
Code: Select all
 +-----------+--------------+-----------+
 | 1  489 7  | 45  2    589 | 3 69  689 |
 | 6  3   2  | 7   89   1   | 4 5   89  |
 | 49 489 5  | 6   3489 389 | 1 7   2   |
 +-----------+--------------+-----------+
 | 3  49  8  | 2   69   7   | 5 1   46  |
 | 7  1   69 | 45  469  59  | 8 2   3   |
 | 5  2   46 | 38  1    38  | 9 46  7   |
 +-----------+--------------+-----------+
 | 2  6   1  | 389 38   4   | 7 39  5   |
 | 49 7   3  | 1   5    2   | 6 8   49  |
 | 8  5   49 | 39  7    6   | 2 349 1   |
 +-----------+--------------+-----------+

X-chain : (9)r4c5=r4c2-r5c3=r9c3-r8c1=r3c1 => -9r3c5
Code: Select all
 +-----------+--------------+-----------+
 | 1  489 7  | 45  2    589 | 3 69  689 |
 | 6  3   2  | 7   89   1   | 4 5   89  |
 | 49 489 5  | 6   3489 389 | 1 7   2   |
 +-----------+--------------+-----------+
 | 3  49  8  | 2   69   7   | 5 1   46  |
 | 7  1   69 | 45  469  59  | 8 2   3   |
 | 5  2   46 | 38  1    38  | 9 46  7   |
 +-----------+--------------+-----------+
 | 2  6   1  | 389 38   4   | 7 39  5   |
 | 49 7   3  | 1   5    2   | 6 8   49  |
 | 8  5   49 | 39  7    6   | 2 349 1   |
 +-----------+--------------+-----------+

X-chain: (9)r2c9=r2c5-r4c5=r4c2-r5c3=r9c3-r8c1=r8c9 => -9r1c9
Code: Select all
 +-----------+-------------+----------+
 | 1  489 7  | 45  2   589 | 3 69  68 |
 | 6  3   2  | 7   89  1   | 4 5   89 |
 | 49 489 5  | 6   348 389 | 1 7   2  |
 +-----------+-------------+----------+
 | 3  49  8  | 2   69  7   | 5 1   46 |
 | 7  1   69 | 45  46  59  | 8 2   3  |
 | 5  2   46 | 38  1   38  | 9 46  7  |
 +-----------+-------------+----------+
 | 2  6   1  | 389 38  4   | 7 39  5  |
 | 49 7   3  | 1   5   2   | 6 8   49 |
 | 8  5   49 | 39  7   6   | 2 349 1  |
 +-----------+-------------+----------+

XY-chain: (4=5)r1c4-(5=4)r5c4-(4=6)r5c5-(6=9)r4c5-(9=4)r4c2 => -4r1c2
stte
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