The New Sudoku Players' Forum

[pingu]

hello my friends , so I started recently doing sudokus and now I am trying to learn a bit new little techniques that can help me solving the puzzles.
So I figured 1 elimination but I don't even know the name of it



so the 7 and 6 blue tile is my starting point that I used to eliminate the 7 on the red tile

[SpAce]

hello my friends , so I started recently doing sudokus and now I am trying to learn a bit new little techniques that can help me solving the puzzles.
So I figured 1 elimination but I don't even know the name of it so the 7 and 6 blue tile is my starting point that I used to eliminate the 7 on the red tile

Hard to say since we don't know the exact logic you used. I see an S-Wing there:

S-Wing: (7)r3c9 = r3c7 - (7=6)r8c7 - r7c9 = (6)r5c9 => -7 r5c9

[pingu]

the logic is to imagine on the blue tile if is a 7 or a 6 both ways eliminates the 7 on the red tile.
Is it a s wing i have never heard of that before

[SpAce]

the logic is to imagine on the blue tile if is a 7 or a 6 both ways eliminates the 7 on the red tile

I see that much, and it's valid logic. However, the exact name of the move depends on the paths you take. The name doesn't really matter, though, as long as the logic is correct -- and it is! It's much more valuable to learn such fundamental deduction techniques than to memorize a bunch of named patterns. So, I think you're on the right path!

The technique you used is a basic kind of Forcing Chain, where you start with two options (at least one of which must be true) and find a common elimination for both of them. One way to present it as such (using the S(plit)-Wing path):

(6)r8c7 - (6)r7c9 = (6)r5c9 [- (7)r5c9]
||
(7)r8c7 - (7)r3c7 = (7)r3c9 [- (7)r5c9]

=> -7 r5c9

Such two-way forcing chains are also automatically AICs (Alternating Inference Chains) if you "pull it straight" into a single chain (and preferably leave out the bracketed eliminations at the ends). That's how I originally presented it. An AIC proves that either the start or the end node must be true (or both), so anything they both see can be eliminated.

Btw, if you want to learn about the Eureka-notation used here, here's a link to the basics.

One more thing. It would be very helpful if you posted your puzzles in a format that can be copy-pasted into a software solver. In this case it didn't matter because I could immediately see the chain in your image, but it might not always be the case. Seems that you're using Hodoku yourself (good), and it's very easy to do with it. Just pull two things from the Edit-menu and attach them to your post: "Copy Givens" (the starting grid as an 81-character string) and "Copy Candidates" (the current puzzle state). Also, put at least the latter into a "Code-block" so it doesn't look mangled. Like this:

The original puzzle (via "Edit::Copy Givens"):

Code: Select all

9....73......6.4...413.9...7....584..3.....1..826....5...5.419...5.8......47....8

The puzzle state (via "Edit::Copy Candidates"):

Code: Select all

.------------.--------------.---------------.
| 9   5    8 | 24  24   7   | 3    6    1   |
| 2   7    3 | 18  6    18  | 4    5    9   |
| 6   4    1 | 3   5    9   | 27   8    27  |
:------------+--------------+---------------:
| 7   1    6 | 29  239  5   | 8    4    23  |
| 5   3    9 | 48  47   28  | 267  1    267 |
| 4   8    2 | 6   17   13  | 9    37   5   |
:------------+--------------+---------------:
| 8   26   7 | 5   23   4   | 1    9    36  |
| 13  269  5 | 19  8    236 | 67   237  4   |
| 13  269  4 | 7   19   236 | 5    23   8   |
'------------'--------------'---------------'


Both of them can be directly copy-pasted into Hodoku.

[pingu]

thank you = ]
I saw that format in this forum but I didn't know how to do it, some techniques seem to be trial error rather than patterns, can you tell me useful techniques that I should learn in first place.

[tarek]

Hi pingu,

You can use an XY wing: r6c8 and r3c9 are linked by r4c9.. Like the jaws of a pincer they both see your target cell r5c9 eliminating the 7. if r5c9 is 7 then you will end up with only 2 possible candidates to fill 3 cells which is impossible.

[Edit: Typo fix. Thanks Space]

[SpAce]

thank you = ]

You're welcome!

some techniques seem to be trial error rather than patterns, can you tell me useful techniques that I should learn in first place.

The single most useful technique in manual solving is coloring. It combines the power of pincer patterns and T&E (trial and error), which are two sides of the same coin anyway, so it's very effective if you know how to use it. If you want to solve non-basic puzzles with the least amount of studying, I recommend starting with coloring because it requires the least memorization and pattern recognition. It's also more effective and elegant than simple T&E. Based on how you used the two paths emanating from the (67) cell to find a common elimination, I think the principles of coloring should be easy for you.

Once you have that generic tool in your bag and understand how it works, then it's much easier to study various patterns as well. I can give some tips about their priorities as well, but first things first. With a good generic tool you're not forced to memorize a zillion specific patterns, but they're useful to study anyway.

You can use an XY wing: r6c8 and r3c9 are linked by r4c9.. Like the jaws of a pincer they both see your target cell r5c9 eliminating the 7. if r5c9 is 7 then you will end up with only 2 possible candidates to fill 3 cells which is impossible.

As tarek explains, XY-Wing is an example of a common and simple pincering pattern (and so is the S-Wing you apparently used without knowing its name, though less common and well-known). It's one of those you should learn to recognize because it's so ubiquitous, but even that is not absolutely necessary as it's actually a short chain which coloring can easily reveal. Also, in the last sentence tarek demonstrates what I said about pincer patterns and T&E being two sides of the same coin: if you find a pincer elimination, you can always double-check that by assuming the eliminated candidate true and seeing that it produces a contradiction (that's T&E). Similarly, it's always possible to find a corresponding pincer pattern for an elimination found via contradiction.

So, there's basically just two fundamental principles you need to understand to find eliminations: pincering and contradictions, and even they're not that different (despite some purists' claims). Coloring can be used to find both kinds without knowing a single pattern (which are just prepackaged pieces of the same principles).

[pingu]

yes, I understand what you mean pincering looks better than contradictions, I feel like contradictions you kinda took a path that is kind of cheating and then you find the number that solves everything and removes the fun but it depends.

ok lets try this

Code: Select all

..19.8.32.2....8.....6.........4..59.1..8..7.94..1.........2.....5....6.83.5.49..

Code: Select all

.-------------------.---------------.------------------.
| 467   567   1     | 9    57   8   | 4567  3    2     |
| 367   2     379   | 4    357  137 | 8     19   1567  |
| 347   5789  34789 | 6    2    137 | 457   149  1457  |
:-------------------+---------------+------------------:
| 237   78    2378  | 237  4    6   | 1     5    9     |
| 5     1     236   | 23   8    9   | 2346  7    346   |
| 9     4     2367  | 237  1    5   | 236   28   368   |
:-------------------+---------------+------------------:
| 1467  679   479   | 18   79   2   | 3457  48   34578 |
| 124   79    5     | 18   379  37  | 24    6    48    |
| 8     3     27    | 5    6    4   | 9     12   17    |
'-------------------'---------------'------------------'


ok it worked , so I found what I believe that is a XY-Wing r6c8 r7c8 and r8c7 that eliminate the 2s above, this seems to be a very powerful technique whats the difference of W-wings and XY-Wings

[SCLT]

There's a 4/8 pair in box 9 - after removing 4 and 8 from other cells in that box the puzzle solves using only singles.

[pingu]

There's a 4/8 pair in box 9 - after removing 4 and 8 from other cells in that box the puzzle solves using only singles.

yes I see it sometimes i have trouble to find hidden stuff in this case is not

[SpAce]

ok it worked , so I found what I believe that is a XY-Wing r6c8 r7c8 and r8c7 that eliminate the 2s above, this seems to be a very powerful technique

You're right. Of course SCLT is also right about not needing it, but it's still a valid XY-Wing. There's no law that says you can't use advanced techniques until all basics are exhausted! I do that all the time, because things like URs and single-digit patterns are often much easier to see than triples and quads, especially without candidates. That's not true here, though.

whats the difference of W-wings and XY-Wings

They're both explained in the Hodoku link. Very different patterns. W-Wing has two bivalue cells with the same two digits (which makes them easy to look for), and a bilocation strong link on one of the digits to connect them (proving that the other digit must be true in at least one of the bivalue cells). The pattern has a total of four cells in its basic form, and it uses only two digits. XY-Wing has three bivalue cells with a total of three digits. It's the shortest possible XY-Chain in a vanilla sudoku. Personally I find W-Wings easier to spot, but opinions vary.

What W-Wings, XY-Wings, and the previously mentioned S-Wings have in common is three strong links ('=') in the chain form:

Code: Select all

W-Wing:  (a=b) - b = b - (b=a) => -a (cells visible to both ends)
XY-Wing: (a=b) - (b=c) - (c=a) => -a (cells visible to both ends)
S-Wing:  a = a - (a=b) - b = b => -a, -b (the opposite end cell)

The three strong links is what makes them "wings". Other members of the one-letter wing-family are M-Wings, L-Wings, and H-Wings, but like S-Wings, they're not as well known as XY-Wings and W-Wings. They all have different link configurations.

Quite confusingly, there's also a totally different wing-family: the (VW)XY(Z)-Wings which are special cases of ALS-XZ patterns. XY-Wings are the only ones that belong to both wing-families. (Logically they should be called just Y-Wings in the one-letter-wing context.)

[pingu]

now I just started coloring the cells I feel like cheating because now i can do everything like brute force
ok so guys imagine this I have 1 cell with 2 possibilities then I try both paths 1 takes me somewhere in the puzzle lets just say a place that there are 3 candidates and it guarantees me a number the other path takes me there and eliminates another of those numbers so it can be eliminated whats the name of this, but I dont really enjoy this way is there a way to see the numbers positions and immediately calculate what is needed

[SpAce]

now I just started coloring the cells I feel like cheating because now i can do everything like brute force

Yeah, it does feel like cheating with easy puzzles. It's still pretty far from brute force. Also, rest assured -- it won't enable you to do everything With more difficult puzzles you still need to know or to figure out a bunch of other tricks to get anywhere. Of course it helps then too.

ok so guys imagine this I have 1 cell with 2 possibilities then I try both paths 1 takes me somewhere in the puzzle lets just say a place that there are 3 candidates and it guarantees me a number the other path takes me there and eliminates another of those numbers so it can be eliminated whats the name of this, but I dont really enjoy this way is there a way to see the numbers positions and immediately calculate what is needed

I don't really understand what you're asking. How about some punctuation to make it more readable? An illustrated example would be helpful too.