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Hey there, I’ve been working on this puzzle for a while now and I think I tried every possible techniques and still can’t move forward anymore. Any idea what’s the next logic step other than guessing a random number? Thanks!

I entered your puzzle in the Hodoku program. I let Hodoku solve the puzzle. It said an 2-String Kite was next in the solution path.

Here's a video I did on 2-String Kites:

https://www.youtube.com/watch?v=3FuofsR2mTY&t=504s

Hodoku also listed there was an XY-Chain in the puzzle. I haven't worked with these yet. I'm currently working on a video for the Swordfish technique. Here is a good Wiki on Sudoku techniques:

http://hodoku.sourceforge.net/en/tech_intro.php

Good Luck!

XY-Chain: 5 5- r1c9 -7- r1c6 -1- r3c5 -9- r3c3 -5- r3c8 -7- r6c8 -5 => r3c8,r456c9<>5

Immediately obvious is Locked Candidates (5) 'Claiming' at r2c46 and a 2 String Kite (6) in c3 and r4. Both lead to eliminations of candidates.

You will need a small xy-chain here.
(5=9)r3c3 - (9=1)r3c5 - (5=7)r1c6 - (7=5)r1c9 => -5r1c23,r3c8
In words:
Either there is 5 in r3c3,
or r3c3=9,r3c5=1,r1c6=7 and r1c9=5
So 5 must be in r3c3 or in r1c9, and can be eliminated from r1c23 and r3c8.

You can also spot the 17 and 19 in box 2 (not both can be 1), so either r1c6 must be 7 and r1c9=5 or r3c5=9 and r3c3=5.

A picture is worth a thousand words.

Code: Select all

*-----------------------------------------------*
| 12679 125  a569 | 1679 8     17-6 | 4 3  57   |
| 67    8     4   | 567  3     567  | 9 2  1    |
| 179   3     59  | 4    19    2    | 6 57 8    |
|-----------------+-----------------+-----------|
|c169   15    7   | 8    2    d156  | 3 4  59   |
| 129   1245  3   | 1579 1459  157  | 8 6  2579 |
| 8     245  b569 | 5679 459   3    | 1 57 2579 |
|-----------------+-----------------+-----------|
| 3     6     2   | 15   15    8    | 7 9  4    |
| 5     9     1   | 3    7     4    | 2 8  6    |
| 4     7     8   | 2    6     9    | 5 1  3    |
*-----------------------------------------------*

This is the two Stringed Kite mentioned above in cells a-b-c-d. One of cells a or d must be 6 so r1c6 <> 6.

Code: Select all

*------------------------------------------------*
| 12679 125   569 | 1679  8    a17  | 4  3  5-7  |
| 67    8     4   | 567   3     567 | 9  2  1    |
| 179   3    c59  | 4    b19    2   | 6 d57 8    |
|-----------------+-----------------+------------|
| 169   15    7   | 8     2     156 | 3  4  59   |
| 129   1245  3   | 1579  1459  157 | 8  6  2579 |
| 8     245   569 | 5679  459   3   | 1  57 2579 |
|-----------------+-----------------+------------|
| 3     6     2   | 15    15    8   | 7  9  4    |
| 5     9     1   | 3     7     4   | 2  8  6    |
| 4     7     8   | 2     6     9   | 5  1  3    |
*------------------------------------------------*

An XY chain in cells a-b-a-c. Again one of cells a or d must be 7, so r1c9 <> 7 = 5. Singles then get you to here :

Code: Select all

*------------------------------------------*
| 12679 12   c69 | 1679  8    17  | 4 3 5  |
| 67    8     4  | 567   3    567 | 9 2 1  |
|b19    3     5  | 4    a19   2   | 6 7 8  |
|----------------+----------------+--------|
| 16    15    7  | 8     2    156 | 3 4 9  |
| 129   1245  3  | 1579  1459 157 | 8 6 27 |
| 8     24   d69 | 679   4-9  3   | 1 5 27 |
|----------------+----------------+--------|
| 3     6     2  | 15    15   8   | 7 9 4  |
| 5     9     1  | 3     7    4   | 2 8 6  |
| 4     7     8  | 2     6    9   | 5 1 3  |
*------------------------------------------*

Another two stringed Kite => r6c5 <> 9 = 4 and the puzzle solves in singles from there.

Leren

Here's an instructional video I did on 2-String Kite:

https://www.youtube.com/watch?v=3FuofsR2mTY&t=504s

I haven't worked with XY-Chain yet but here's a wiki page on it:

http://hodoku.sourceforge.net/en/tech_chains.php