Sudoku Explorer "Strong Links"

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Sudoku Explorer "Strong Links"

Postby Pupp » Fri Sep 11, 2020 2:56 pm

I actually solved this puzzle fairly easily, but I was curious so I put it through SE and it said it had "1 x 3 Strong Links"

I was wondering exactly what that meant. [No need to solve this puzzle, I'm just asking a general question.]

Obviously I used different logic to solve the puzzle than SE did. So I"m not asking about that. Just what "Strong Links" in SE means.
I used a few techniques to solve it. I notice that SE tends to use the easiest techniques it can find, then use as few harder techniques it can find. At the time I was waiting for my car to be washed and detailed, so I wasn't memorizing every technique I might have used. Plus I suck at trying to remember every trick I used when there is more than a single point in the game that makes the rest of the puzzle trivial. There are probably several ways to solve this particular puzzle.

.2.8.9...
..8..2..3
..9.6.84.
69......4
..5.2.9..
8......25
.83.7.4..
1..6..2..
...4.8.1.

+-------------------+-------------------+-------------------+
| 3457 2 1467 | 8 1345 9 | 1567 567 167 |
| 457 14567 8 | 157 145 2 | 1567 5679 3 |
| 357 1357 9 | 1357 6 1357 | 8 4 127 |
+-------------------+-------------------+-------------------+
| 6 9 127 | 1357 1358 1357 | 137 378 4 |
| 347 1347 5 | 137 2 13467 | 9 3678 1678 |
| 8 1347 147 | 1379 1349 13467 | 1367 2 5 |
+-------------------+-------------------+-------------------+
| 259 8 3 | 1259 7 15 | 4 569 69 |
| 1 457 47 | 6 359 35 | 2 35789 789 |
| 2579 567 267 | 4 359 8 | 3567 1 679 |
+-------------------+-------------------+-------------------+

This Sudoku can be solved using the following logical methods:
51 x Hidden Single
1 x Naked Single
6 x Pointing
2 x Claiming
1 x Hidden Pair
2 x Skyscraper
1 x XY-Wing
1 x 3 Strong links (including blocks) 2102 (Using 2 grouped strong links)
The most difficult technique (ER): 3 Strong links (including blocks) 2102 (Using 2 grouped strong links)
Pupp
 
Posts: 157
Joined: 18 October 2019

Re: Sudoku Explorer "Strong Links"

Postby mith » Fri Sep 11, 2020 6:53 pm

Code: Select all
+---------------+-------------+----------------+
| 3   2    b467 | 8   14  9   | 5    c67  c17  |
| 457 467  8    | 57  14  2   | d167 9    3    |
| 57  1    9    | 3   6   57  | 8    4    2    |
+---------------+-------------+----------------+
| 6   9    2    | 157 8   57  | 17   3    4    |
| 47  3    5    | 17  2   46  | 9    678  178  |
| 8   f47  1    | 9   3   46  | e67  2    5    |
+---------------+-------------+----------------+
| 9   8    3    | 2   7   1   | 4    5    6    |
| 1   45-7 a47  | 6   59  3   | 2    78   789  |
| 2   56-7 a67  | 4   59  8   | 3    1    79   |
+---------------+-------------+----------------+


This is a chain restricted to one value (7). As an AIC, it would look something like this (which could probably make do with more compact notation, but anyway):

(7r8c3 | 7r9c3 ) = 7r1c3 - (7r1c8 | 7r1c9) = 7r2c7 - 7r6c7 = 7r6c2 => -7r89c2

Both ends of the chain imply 7 cannot be in r89c2, and the alternative strong/weak links proves one end of the chain must be true.

If 7 is in r89c3, it can't be in r89c2.
If 7 is not in r89c3, there must be a 7 in r1c3,
so there can't be a 7 in r1c89,
so there must be a 7 in r2c7,
so there can't be a 7 in r6c7,
so there must be a 7 in r6c2,
so there can't be a 7 in r89c2.

A Skyscraper, would be an example of a 2 strong link technique. (The "grouped" term comes from using multiple cells in a row/column/block as part of the link; here, r89c3 and r1c89 are grouped.)
mith
 
Posts: 369
Joined: 14 July 2020

Re: Sudoku Explorer "Strong Links"

Postby Pupp » Fri Sep 11, 2020 7:07 pm

Ahh, ok. I use techniques like that. I didn't on this particular puzzle though. I try to exhaust other techniques before using a forcing chain or alternating interference chains, etc. Plus I notice I tend to use a variety of middling techniques to solve puzzles. I'm sure as I get harder puzzles, I'll be forced to use the hardest techniques, but I suspect I'll rarely solve a puzzle the way SE wants to.

I suppose that why I like sudoku: as I get harder puzzles, I get to expand my creativity in solving puzzles, and never tried to emulate the steps a solver might use.
Pupp
 
Posts: 157
Joined: 18 October 2019

Re: Sudoku Explorer "Strong Links"

Postby mith » Fri Sep 11, 2020 9:21 pm

Yeah, there are almost always alternative paths. Hodoku for example solves this one with a Hidden Rectangle (78r58c89 => -7r5c9) and a Finned Jellyfish (-7r5c8)... and actually the Hidden Rectangle is redundant because the Finned Jellyfish will eliminate both.
mith
 
Posts: 369
Joined: 14 July 2020


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