Best solving technique for this?

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Best solving technique for this?

Postby Madolite » Tue Dec 11, 2018 12:53 am

Hey, I'm getting stuck at these "Harder" (e.g. see Example below) and "Hardest" puzzles on Sudoku Epic (program), and I'm wondering what the best method is for solving this particular problem, where I can't seem to find anything that looks like any wing pattern. I could be wrong, but it looks like all the doubles, triples etc are just all hermetically sealed in some way. Do I need to look for AIC in these kinds of mid-game puzzles? Is that the only solution? Thanks.

NB: If there's a wing pattern here, I'd love to hear about it cause I've just barely gotten into those. I'm fairly certain there is no useful X-wing here (I only found c1r4-c8r6 and some other potential wing at c6r7-c7r9). Is there something in c6r7-c7r9? That's my first thought.
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Re: Best solving technique for this?

Postby Madolite » Tue Dec 11, 2018 1:20 am

(Edit) Partial Solution:
I discovered this as I was brainstorming:

If the red box (c3) contains a 2, then the blue triple (c9) must be 876. Thus a 4 can be excluded.
Similarly, if the red box contains an 8, then the blue triple must be 276, due to r1 and r3 becoming a 26 double (and r2 becoming 7) - which also excludes the 4.
Therefore, the 4 in block 3 must go into c7r3.
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Re: Best solving technique for this?

Postby Madolite » Tue Dec 11, 2018 1:40 am

This solution actually solved my puzzle entirely. :D
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Re: Best solving technique for this?

Postby SpAce » Tue Dec 11, 2018 2:26 am

Hi Madolite.

Madolite wrote:Do I need to look for AIC chains in these kinds of mid-game puzzles? Is that the only solution?

No and yes. These kinds of puzzles can be solved with pretty simple named patterns. However, most of them are actually short AICs, so understanding the underlying principles of AICs makes finding and using those simpler patterns easier as well. In fact, you don't have to know their names or specific shapes and types if you can find any generic chains. That's how I learned to solve non-basic puzzles. I learned specific patterns and their names later, not because it was necessary for solving but because it made communication with others easier (and it also helps to spot those special cases faster).

NB: If there's a wing pattern here, I'd love to hear about it cause I've just barely gotten into those.

Not sure what you mean by "wing pattern". As far as I'm concerned, X-Wings aren't really wings at all despite the name (it's a misnomer, because they're really fishes or single-digit loops). Things like W-Wings and XY-Wings are the most common and easiest to spot simple wings by the definition I've adopted (a simple multi-digit AIC with three strong links). More complex and rarely used simple wings are M-Wings, L-Wings, H-Wings, and S-Wings, but I wouldn't worry about them (I just see them as short AICs, and only look up the name if I really feel like it). Then there are XYZ-Wings and even (UV)WXYZ-Wings which are actually special cases of ALS-techniques, so I don't really see them in the same family as the simple wings.

I'm fairly certain there is no useful X-wing here

You're both wrong and right. There's an active X-Wing on 2s (r17\c39) which would eliminate 2r3c9. It's a pretty useless elimination, however, so from that point of view it's true that there's no useful X-Wing here.

(I only found c1r4-c8r6

You're right, that's a dud X-Wing. Btw, please say r4c1 instead of c1r4. That's easier to read for most of us here.

and some other potential wing at c6r7-c7r9). Is there something in c6r7-c7r9? That's my first thought.

There's no wing there, but you're right that there's something. It's a Unique Rectangle Type 1 -- probably the easiest non-basic pattern and one you should definitely learn first, imho, because it's very common and often effective. In this case it would allow you to eliminate 4 and 5 from r9c7, leaving there just 1. That would be quite useful, because you'd get several placements as a result, but it wouldn't solve the whole puzzle.

Other than that, most of what I just said here applies to this puzzle as well. There are several patterns/techniques available that would reduce the puzzle to singles, including a couple of Skyscrapers (on 7s). Other single-digit possibilities are 2-String Kites and Empty Rectangles (both on 7s as well), and Simple Coloring would work too. Also a couple of W-Wings (27) and (67).

The easiest effective technique for me would be Skyscraper, but since I just showed an example of that for the linked puzzle, here's a W-Wing (27) solution for this one:

Code: Select all
.------------------.------------.----------------.
| 5     4    a(2)7 | 3  8   b67 | 9    1   267   |
| 6     78     1   | 2  4    9  | 3    5   78    |
| 9     78-2   3   | 5  67   1  | 47   28  24678 |
:------------------+------------+----------------:
| 24  d(2)7    9   | 1  5   c67 | 8    46  3     |
| 3     6      5   | 4  2    8  | 17   9   17    |
| 48    1      78  | 9  67   3  | 2    46  5     |
:------------------+------------+----------------:
| 7     9      28  | 6  1    45 | 45   3   28    |
| 1     5      4   | 8  3    2  | 6    7   9     |
| 28    3      6   | 7  9    45 | 145  28  14    |
'------------------'------------'----------------'

W-Wing[27]: (2=7)r1c3 - (7)r1c6 = (7)r4c6 - (7=2)r4c2 => -2 r3c2; stte

And here's the other one (67) with two eliminations:

Code: Select all
.--------------.----------------.----------------.
| 5   4    c27 | 3  8     d(6)7 | 9    1   267   |
| 6   78    1  | 2  4       9   | 3    5   78    |
| 9   278   3  | 5  7-6     1   | 47   28  24678 |
:--------------+----------------+----------------:
| 24  27    9  | 1  5       7-6 | 8    46  3     |
| 3   6     5  | 4  2       8   | 17   9   17    |
| 48  1    b78 | 9  a(6)7   3   | 2    46  5     |
:--------------+----------------+----------------:
| 7   9     28 | 6  1       45  | 45   3   28    |
| 1   5     4  | 8  3       2   | 6    7   9     |
| 28  3     6  | 7  9       45  | 145  28  14    |
'--------------'----------------'----------------'

W-Wing[67]: (6=7)r6c5 - (7)r6c3 = (7)r1c3 - (7=6)r1c6 => -6 r3c5,r4c6; stte

Imho, W-Wing is the easiest multi-digit pattern to spot, because its signature is two cells with the same two candidates, connected by a short symmetric chain. Some would say XY-Wing is the easiest because it has all bivalue cells, but it's non-symmetric with three different digits. You can learn about W-Wings (and XY-Wings) here.

Btw, I see that you've found a solution on your own while I was typing this. Great! I'll review that shortly. Anything I said above should still be valid anyway.
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
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Re: Best solving technique for this?

Postby SpAce » Tue Dec 11, 2018 3:01 am

Madolite wrote:(Edit) Partial Solution:
I discovered this as I was brainstorming:

If the red box (c3) contains a 2, then the blue triple (c9) must be 876. Thus a 4 can be excluded.
Similarly, if the red box contains an 8, then the blue triple must be 276, due to r1 and r3 becoming a 26 double (and r2 becoming 7) - which also excludes the 4.
Therefore, the 4 in block 3 must go into c7r3.

Sorry, but I can't follow your logic. 4r3c3 is a valid elimination and can be proved with a variety of pretty simple chains, but I don't see how yours does it. The case with 2r7c3 works as it forms a hidden pair (26)r13c9 which would eliminate the 4r3c9. However, I don't see how the case 8r7c3 works (or I do, but not the way you explained it). You have the right idea, though.

This solution actually solved my puzzle entirely. :D

I don't see how that would happen either. Even if you eliminate 4r3c9, basics won't solve the puzzle from that point. Note that the UR I mentioned earlier would also get the same result, but like I said, it doesn't solve puzzle.
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Re: Best solving technique for this?

Postby Madolite » Tue Dec 11, 2018 7:50 am

This solution actually solved my puzzle entirely. :D

I don't see how that would happen either. Even if you eliminate 4r3c9, basics won't solve the puzzle from that point. Note that the UR I mentioned earlier would also get the same result, but like I said, it doesn't solve puzzle.


I just meant that the puzzle could now be solved without much effort, that's all. But you're right, I made a mistake with the ramifications of 8r7c3 => 2r3c8 so I would be wrong, either way, even if I meant it loosely. I think I saw something that wasn't there, with the 8 remaining in r2c9 only, or something (which is incorrect). Either way, I'm too tired right now to look at it, but I'll take a look at those skyscraper patterns and consider what you said, for future puzzles. Practice makes perfect, as they say. And I definitely need to practice my spotting and double-checking.

Thanks again. ;)
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Re: Best solving technique for this?

Postby SpAce » Tue Dec 11, 2018 9:53 am

Got it, and no problem!
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