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https://imgur.com/a/3SUtQUU I'm not actually a beginner. This app has 4 difficulty settings: Easy, Medium, Hard and Expert. Hard is easy for me but Expert is impossible. I can't make progress so at last I tought that I need help. Please help me and explain every step.

b3 {1,4,9}
==> (5,6) b3\r1
solves r1c3

Pat actually gave you the hardest step (*) of this puzzle, but it's not all you have left. I would recommend taking the easier pickings first and save the hidden triple/naked quad last, after which it's singles to the end. Of course you can use it earlier if you happen to spot it, but it's not the natural progression to look for those when you still have pointing pairs and naked triples around (*). In this case taking it early may actually make things a bit harder as it reveals an unhelpful extra naked triple.

(*) Added: this ordering only applies if pencil marks are being used -- otherwise hidden triples are easier than naked triples.

So, you're currently here:

Code: Select all

.--------------------.------------------.--------------------.
| 4     23578-6  356 | 9      3678  1   | 258  56     568    |
| 389   2389-6   136 | 2348   368   5   | 28   7      14689  |
| 5789  25789-6  156 | 248    678   468 | 3    14569  145689 |
:--------------------+------------------+--------------------:
| 135  *35(6)    8   | 13     9     36  | 4    2      7      |
|%(13) *4(6)-3   2   | 48-13  68-3  7   | 9  %(135) %(135)   |
| 139   349      7   | 5      2     34  | 6    8      13     |
:--------------------+------------------+--------------------:
| 6     78       35  | 78     4     9   | 1    35     2      |
| 3578  3578     4   | 6      1     2   | 578  359    3589   |
| 2     1        9   | 378    5     38  | 78   46     468    |
'--------------------'------------------'--------------------'

There's an unexecuted pointing pair (6)r56c2 (*), as well as a naked triple (135)r5c189 (%). I've shown their eliminations. The naked triple is important, because it gives you lots of further eliminations and placements:

-> Hidden single (1)r4c4
-> Pointing pair (3)b5/c6 -> -3 r9c6
-> Naked singles (8)r9c6, (7)r7c4, (3)r9c4, (2)r7c2, (7)r9c7

[Added: As eleven points out below, the eliminations of the naked triple (135) can also be seen through its coupled hidden triple (468), which is easier to spot if pencil marks aren't being used.]

After that you're here, and now is the time to look for more difficult patterns like the hidden triple/naked quad:

Code: Select all

.-------------------.---------------.------------------------.
| 4     237-5  3-56 | 9    378-6  1 |*2(5)8 *(56)  *(56)8    |
| 389   239    136  | 248  368   5  |*28     7       149-68  |
| 5789  2579   156  | 248  678   46 | 3      149-56  149-568 |
:-------------------+---------------+------------------------:
| 35    356    8    | 1    9     36 | 4      2       7       |
| 13    46     2    | 48   68    7  | 9      135     135     |
| 139   349    7    | 5    2     34 | 6      8       13      |
:-------------------+---------------+------------------------:
| 6     8      35   | 7    4     9  | 1      35      2       |
| 357   357    4    | 6    1     2  | 58     359     3589    |
| 2     1      9    | 3    5     8  | 7      46      46      |
'-------------------'---------------'------------------------'

Look at box 3. There are 7 empty cells and thus 7 digits missing. Luckily, they happen to form two subsets 4+3: a naked quad (2568) and a hidden triple (149), which means we can eliminate the extra candidates from the hidden set. Pat implicated only the hidden triple, but since you're solving with candidates, it's probably easier to see the naked quad (but it depends on your solving style). Without candidates the hidden triple would definitely be the easier, because you can see that the givens (149) in both row 1 and column 7 leave only three places for those digits in box 3.

Either way you get the same eliminations in the box, but with the hidden triple approach you then have to perform two pointing pair/triple operations with the now locked (5) and (6) in r1c789. Using the naked quad would actually give you both the box and the row eliminations in a single move (but that's a bit advanced way of seeing it). After that it's singles to the end.

If you learn to spot the last move yourself, you can congratulate yourself. It's pretty much the third hardest basic move there is. The only things harder would be a naked quad/hidden quad pairing and the very rare naked quin/hidden quad pairing. Even though they're counted as basic moves, I'd say they're often harder to spot than some "advanced" moves (especially Unique Rectangles and X-Wings which are almost trivial compared to these).

Here is, how you can spot the hidden triple in your grid without pencilmarks:

Code: Select all

 +-------+-------+-------+
 |*4 . . |*9 .*1 | - - - |
 | . . . | . . 5 | - 7 x |
 | . . . | . . . | 3 x x |
 +-------+-------+-------+
 | . . 8 | . 9 . |*4 2 7 |
 | . . 2 | . . 7 |*9 . . |
 | . . 7 | 5 2 . | 6 8 . |
 +-------+-------+-------+
 | 6 . . | . 4 9 |*1 . 2 |
 | . . 4 | 6 1 2 | . . . |
 | 2 1 9 | . 5 . | . . . |
 +-------+-------+-------+

And look for 78 in columns 38, which gives you a hidden pair in r7.
And 46 in rows 78 and column 7.
Harder to spot 468 in box 6, and c1/box3 for row 5 ...

eleven wrote:And look for 78 in columns 38, which gives you a hidden pair in r7.
And 46 in rows 78 and column 7.
Harder to spot 468 in box 6, and c1/box3 for row 5 ...

Good stuff. Without pencil marks, hidden subsets are naturally much easier to find than naked ones, and having no pm cluttering the grid actually makes it even easier. Also, I think the hidden triple in box 3 is probably easiest to spot before any placements because the crossing of (149)r1&c7 is most visible then (so perhaps my earlier recommendation to save it for the last isn't good for no-pm solving).

That being said, this puzzle is right on the edge of my not-so-great no-pm solving skills. I did successfully test-solve it without pm, but that was after knowing the tougher parts so it doesn't really count. Nevertheless, I'm pretty sure I would have eventually spotted the two hidden triples and their implications, but I'm not certain I would have had the discipline to not add pm had I got stuck (although I nowadays try to solve all basic puzzles without pm). All other basics I can find more or less certainly without pm, but I'm still often blind to triples and quads (easier if they're box-based and relatively obvious like the 149 here).

Thank you everyone! I can't believe I've missed them all, there's a lot of clues... I was thinking there's some techniques that I don't know about but pointing pairs, naked pairs, hidden pairs I know them all, I even used them in this puzzle so it really shocked me to learn that I couldn't see what you pointed out. Thank you again. I guess I'll have to solve more in order to be able to spot these easier.