The New Sudoku Players' Forum

[yzfwsf]

Code: Select all

.1......582.....3...9.4.......6.8..4.3.12.9.66......2.....8..1...85.....7....2..3

[AnotherLife]

After the basics the sudoku state becomes as follows:

Code: Select all

.--------------.----------------.--------------.
| 34  1    46  | 8   3679  3679 | 2   79   5   |
| 8   2    56  | 79  156   156  | 4   3    79  |
| 35  7    9   | 2   4     35   | 1   6    8   |
:--------------+----------------+--------------:
| 1   9    2   | 6   57    8    | 3   57   4   |
| 45  3    457 | 1   2     457  | 9   8    6   |
| 6   8    457 | 3   579   4579 | 57  2    1   |
:--------------+----------------+--------------:
| 29  456  3   | 47  8     67   | 56  1    29  |
| 29  46   8   | 5   13    13   | 67  479  279 |
| 7   456  1   | 49  69    2    | 8   45   3   |
'--------------'----------------'--------------'


It is possible to prove that r2c6=6 and get a one-step solution, but we need to construct a forcing net, that is, a series of chains. Can we consider this as a one-step solution? I am not sure. I also do not understand why we have to search for a complicated one-step solution when a simple human two-step solution is available.
I found this one manually:
1. Uniqueness Test 1: 2/9 in r7c19,r8c19 => r8c9<>2, r8c9<>9.
2. XY-Wing: 3/5/1 in r2c5,r38c6 => r2c6,r8c5<>1 (after a series of singles).

[Hajime]

After Singles Only you can come to:

Code: Select all

   +-----'----'-----+----'-----'-----+----'----'---+ 
   |  34    1   3467|  8   379   379 |  2  4679  5 | 
   |  8     2   457 | 79   1579   6  | 147   3  179| 
   |  35   567   9  |  2    4    1357| 167  67   8 | 
   +-----'----'-----+----'-----'-----+----'----'---+ 
   | 1259  579  1257|  6   3579   8  |1357  57   4 | 
   |  45    3   457 |  1    2    457 |  9    8   6 | 
   |  6     8   1457|3479  3579 34579|1357   2   17| 
   +-----'----'-----+----'-----'-----+----'----'---+ 
   |23459 4569 23456|3479   8    3479|4567   1  279| 
   |12349  469   8  |  5  13679 13479| 467 4679 279| 
   |  7   4569  1456| 49   169    2  |  8  4569  3 | 
   +-----'----'-----'----'-----'-----'----'----'---+ 
                                                     
#1//B4
.1.8..2.582...6.3...924...8...6.8..4.3.12.98668.....2.....8..1...85.....7....28.3

From here the puzzle is solvable with Basics: Naked/Hidden Pair & Triplets and 3x Pointing/Claiming

With Singles Only and Forcing Net, I need 2x Forcing Nets, not once ....

[Cenoman]

Don't know if the following net is considered as one-step (I guess, in TDP it would be...)
To me, it's a disguised two-stepper

Code: Select all

 +-------------------+---------------------+-------------------+
 |  34   1    c6-4   |  8    3679 AB3679   |  2    79    5     |
 |  8    2    b56    |  79   156   a156    |  4    3     79    |
 |  35   7     9     |  2    4      35     |  1    6     8     |
 +-------------------+---------------------+-------------------+
 |  1    9     2     |  6    57     8      |  3    57    4     |
 |  45   3     457   |  1    2      457    |  9    8     6     |
 |  6    8   zC457   |  3   y579  zC4579   |  57   2     1     |
 +-------------------+---------------------+-------------------+
 |  29   56-4  3     |b'47   8   vb'67     |  56   1     29    |
 |  29 z'46    8     |  5    13     13     |  67   479   279   |
 |  7  y'456   1     |  49 xw69     2      |  8    45    3     |
 +-------------------+---------------------+-------------------+
Kraken row (6)r127c6

(6)r1c6 - (9)r1c6 = (94)r6c36 *
 ||   \
 ||   (6=74)r7c46 **
 ||   /
(6)r2c6 - r2c3 = (6)r1c3 *
 ||                       
 ||                 (9)r9c5 - r6c5 = (94)r6c36 *
 ||               //
(6)r7c6 - (6)r9c5
                  \\
                    (6)r9c2 - (6=4)r8c2 **
------------------------
=> -4 r1c3*, r7c2**; ste

Attempt to write it in lines:
Kraken row (6)r127c6
(6)r1c6 - (9r1c6 | 6r7c6) = (94r6c36 & 74r4c46)
(6)r2c6 - (6r2c3 | 6r7c6) = (6r1c3 & 74r4c46)
(6)r7c6 - r9c5 = (9r9c5 & 6r9c2) - (9r6c5 | 6r8c2) = (94r6c36 & 4r8c2)
------------------------
=> -4 r1c3*, r7c2**; ste

[AnotherLife]

After Singles Only you can come to:

Code: Select all

   +-----'----'-----+----'-----'-----+----'----'---+ 
   |  34    1   3467|  8   379   379 |  2  4679  5 | 
   |  8     2   457 | 79   1579   6  | 147   3  179| 
   |  35   567   9  |  2    4    1357| 167  67   8 | 
   +-----'----'-----+----'-----'-----+----'----'---+ 
   | 1259  579  1257|  6   3579   8  |1357  57   4 | 
   |  45    3   457 |  1    2    457 |  9    8   6 | 
   |  6     8   1457|3479  3579 34579|1357   2   17| 
   +-----'----'-----+----'-----'-----+----'----'---+ 
   |23459 4569 23456|3479   8    3479|4567   1  279| 
   |12349  469   8  |  5  13679 13479| 467 4679 279| 
   |  7   4569  1456| 49   169    2  |  8  4569  3 | 
   +-----'----'-----'----'-----'-----'----'----'---+ 
                                                     
#1//B4
.1.8..2.582...6.3...924...8...6.8..4.3.12.98668.....2.....8..1...85.....7....28.3

From here the puzzle is solvable with Basics: Naked/Hidden Pair & Triplets and 3x Pointing/Claiming

With Singles Only and Forcing Net, I need 2x Forcing Nets, not once ....

As far as I see, the basic steps such as naked/hidden pairs and triples, locked candidates are always ignored on the forum when the task is to find a one-step solution. If the task were to find a one-step solution after Singles Only then one-step solutions might not exist even in very simple cases. As to this example, after Singles Only we can apply a hidden triple (1,2,9 in r478c1 => r47c1<>5, r78c1<>3, r78c1<>4) then, after a sequence of singles, we have a forcing net, and finally the last sequence of singles. I do not see a reason to apply two forcing nets.

By the way, this looks ridiculous when we apply two forcing nets to a simple puzzle.

[Hajime]

As to this example, after Singles Only we can apply a hidden triple (1,2,9 in r478c1 => r47c1<>5, r78c1<>3, r78c1<>4) then, after a sequence of singles....

you allow methods like naked/hidden subsets (and pointing/claiming needed) and then you can finish the puzzle: btte
No Forcing Net needed

[AnotherLife]

you allow methods like naked/hidden subsets (and pointing/claiming needed) and then you can finish the puzzle: btte
No Forcing Net needed

I do not understand what you mean. Will you write the whole one-step solution from the start?

Code: Select all

.1......582.....3...9.4.......6.8..4.3.12.9.66......2.....8..1...85.....7....2..3

[Hajime]

I do not understand what you mean. Will you write the whole one-step solution from the start?

I see your point. And now I cannot repeat the solving process. I am not able to solve 6r2c6 anymore with basic methods. So all my above statements are void.
I will look again into it tomorrow.

[Cenoman]

Hi AnotherLife,

Welcome to this forum !

You wonder how it works. Some months ago, daily simple puzzles were proposed. By simple, I mean solvable in one step after basics, (with "singles to the end" finish as an extra challenge). Basics are the techniques you have in mind: naked and hidden singles, naked and hidden subsets, claiming and pointing, that I call these "lcls" (Locked Candidares, Locked Sets), because the term "basics" is sometimes misused as encompassing other techniques (fishes, wings,...). Recently, other types of puzzles have been proposed, sometimes with an extra challenge (one-step, ste finish, many fish-steps, finding symmetries or exotic patterns), from easy to very hard.

Another predominant practise in the forum is to use Eureka conventions to write chains.
Showing pencimarks is also a common practise.

As regards the puzzle of this thread,

It is possible to prove that r2c6=6 and get a one-step solution, but we need to construct a forcing net, that is, a series of chains. Can we consider this as a one-step solution? I am not sure. I also do not understand why we have to search for a complicated one-step solution when a simple human two-step solution is available.
I found this one manually:
1. Uniqueness Test 1: 2/9 in r7c19,r8c19 => r8c9<>2, r8c9<>9.
2. XY-Wing: 3/5/1 in r2c5,r38c6 => r2c6,r8c5<>1 (after a series of singles).

Your two-step solution is nice!
Proving +6r2c6 is not easy, I'm curious to see the forcing net.

As far as I see, the basic steps such as naked/hidden pairs and triples, locked candidates are always ignored on the forum when the task is to find a one-step solution. If the task were to find a one-step solution after Singles Only then one-step solutions might not exist even in very simple cases. As to this example, after Singles Only we can apply a hidden triple (1,2,9 in r478c1 => r47c1<>5, r78c1<>3, r78c1<>4) then, after a sequence of singles, we have a forcing net, and finally the last sequence of singles. I do not see a reason to apply two forcing nets.

By the way, this looks ridiculous when we apply two forcing nets to a simple puzzle.

Basic steps are omitted by a large part of players, at the start and between significant steps. Readers are supposed to be able to process these themselves, or at least they are supposed to trust the author.

The reason to apply two forcing nets to a simple puzzle here was in yzfwsf's expectation ("One trick pony"). Of course the puzzle is simple and forcing nets are "a sledgehammer to crack a nut". Just a bit more fun !

[AnotherLife]

Proving +6r2c6 is not easy, I'm curious to see the forcing net.

Thanks for your reply, sir.
I will try to show that all three possibilities in row 2 r2c3=6, r2c5=6 and r2c6=6 lead to r2c6=6. See the picture: https://disk.yandex.ru/i/OyvUOCzpX6k-jg
1. The red chains in the picture. r2c3=6 => r1c3<>6 => r1c3=4 => r6c3<>4 => r6c6=4 => r6c6<>9 => r1c6=9 =>
1.1. r1c6<>6
1.2. r2c4<>9 => r9c4=9 => r9c5<>9 => r9c5=6 => r7c6<>6 => (because of 1.1) r2c6=6.
2. The black chains in the picture. r2c5=6 =>
2.1. r1c6<>6
2.2. r2c6<>6 => (because of 2.1) r7c6=6 => r7c7=5 => r6c7<>5
2.3. r2c3<>6 => r2c3=5 =>
2.3.1. r6c3<>5
2.3.2. r3c1<>5 => r3c6=5 => r6c6<>5 => (because of 2.2, 2.3.1) r6c5=5 => r4c5<>5 => r4c8=5 => r9c8<>5 => r9c2=5 =>
r9c2<>6 => r9c5=6 => r2c5<>6 => (because of 2.1) r2c6=6.
3. r2c6=6 => r2c6=6.

I doubt that this forcing net can be taken as a one-step solution. Frankly speaking, this is not my solution, and I just tried to explain the computer inferences in more intelligible terms.

EDIT
I think it is easier to show that the premise r2c6<>6 leads to a contradiction (my above picture remains valid). If r2c6<>6 then either r2c3=6 or r2c5=6.
1. r2c3=6 => (see above) r2c6=6 => r2c3<>6.
2. r2c5=6 => (see above) r2c5<>6.

[jco]

I only found solution with two moves (first one using colouring).

After basics

Code: Select all

  1   2    3     4   5     6      7   8    9
.--------------+----------------+--------------.
| 34  1    46  | 8   3679  3679 | 2   79   5   | 1
| 8   2    56  | 79  156   156  | 4   3    79  | 2
| 35  7    9   | 2   4     35   | 1   6    8   | 3
|--------------+----------------+--------------|
| 1   9    2   | 6   57    8    | 3   57   4   | 4
| 45  3    457 | 1   2     457  | 9   8    6   | 5
| 6   8    457 | 3   579   4579 | 57  2    1   | 6
|--------------+----------------+--------------|
| 29 c456  3   |b47  8    a7-6  | 56  1    29  | 7
| 29  46   8   | 5   13    13   | 67  479  279 | 8
| 7  d456  1   | 49 e69    2    | 8   45   3   | 9
'--------------+----------------+--------------'


1. (7)r7c6=(7-4)r7c4=(4-5)r7c2=(5-6)r9c2=(6)r9c5 => -6 r7c6 (+ 22 placements)

Code: Select all

  1   2  3    4   5     6      7  8  9
.-----------+----------------+---------.
| 34  1  46 | 8  b39    369  | 2  7  5 | 1
| 8   2  56 | 7   1-5   156  | 4  3  9 | 2
| 35  7  9  | 2   4    c35   | 1  6  8 | 3
|-----------+----------------+---------|
| 1   9  2  | 6   7     8    | 3  5  4 | 4
| 45  3  7  | 1   2     4-5  | 9  8  6 | 5
| 6   8  45 | 3  a59    49-5 | 7  2  1 | 6
|-----------+----------------+---------|
| 9   6  3  | 4   8     7    | 5  1  2 | 7
| 2   4  8  | 5   13    13   | 6  9  7 | 8
| 7   5  1  | 9   6     2    | 8  4  3 | 9
'-----------+----------------+---------'

2. XY-Wing (5=9)r6c5-(9=3)r1c5-(3=5)r3c5 => -5 r2c5, -5 r56c6; ste

Without placements in between:

Code: Select all

       1  2    3     4    5     6      7   8    9
    .--------------+-----------------+--------------.
    |e34  1    46  | 8   d3679  3679 | 2   79   5   | 1
    | 8   2   g56  | 79 hb156  a156  | 4   3    79  | 2
    |f35  7    9   | 2    4    a35   | 1   6    8   | 3
    |--------------+-----------------+--------------|
    | 1   9    2   | 6   i57    8    | 3   57   4   | 4
    | 45  3    457 | 1    2     47-5 | 9   8    6   | 5
    | 6   8    457 | 3   i579   4579 | 57  2    1   | 6
    |--------------+-----------------+--------------|
    | 29  456  3   | 47   8     67   | 56  1    29  | 7
    | 29  46   8   | 5   c13    13   | 67  479  279 | 8
    | 7   456  1   | 49   69    2    | 8   45   3   | 9
    '--------------+-----------------+--------------'

1. (5)r13c6=(5-1)r2c5=(1-3)r8c5=(3)r1c5-(3)r1c1=(3-5)r3c1=(5)r2c3-(5)r2c5=(5)r46c5 => -5 r5c6
2. (7)r7c6=(7-4)r7c4=(4-5)r7c2=(5-6)r9c2=(6)r9c5 => -6 r7c6; ste

EDIT: added second solution

[denis_berthier]

Some months ago, daily simple puzzles were proposed. By simple, I mean solvable in one step after basics, (with "singles to the end" finish as an extra challenge). Basics are the techniques you have in mind: naked and hidden singles, naked and hidden subsets, claiming and pointing, that I call these "lcls" (Locked Candidares, Locked Sets), because the term "basics" is sometimes misused as encompassing other techniques (fishes, wings,...).

Hi Cenoman,
I think the term "basic" is always misused and it is always ambiguous. There's no rational reason to make any difference between a naked Pair, a Hidden pair and an X-Wing. Some will argue that an X-Wing is easier to find than a Hidden Pair (I'm not one of those). Note also that some people exclude any kind of Quads from the "basics".

Recently, other types of puzzles have been proposed, sometimes with an extra challenge (one-step, ste finish, many fish-steps, finding symmetries or exotic patterns), from easy to very hard.

Probably, people got bored of seeing always the same patterns.

As far as I can remember, the one-step challenge is not really recent. What's recent is trying to apply it to hard puzzles. In many cases, this leads to totally absurd solutions, where much easier alternative multi-step ones are available. I have proposed a few ones, sometimes with the explicit purpose of showing their absurdity.
Moreover, when the way of finding one-step solutions is revealed, it appears less enticing. The first step is to find an anti-backdoor, a procedure totally similar to finding a backdoor and akin to T&E.

Many-Subset or many-fish puzzles are a novelty also, due to Mith. I don't know if there's an explicit challenge of finding as many ones as possible in his puzzles, but when I see one, I find it fun to proceed that way. It's also a way to pay hommage to his exceptional puzzles.
Given any puzzle, there are generally many very different ways to solve it, with or without additional conditions, and it's generally pointless to discuss which is better.

Hard puzzles in this section may be recent also, but they are interesting for part of us, as they allow to discuss advanced techniques in detail.

[Hajime]

My 2 cents... I did this puzzle over and over with SiSeSuSo (and manually) and sometimes I need a Forcing Net and sometimes not
Here the simple solution without long chains/nets

Code: Select all

Method   \  Sudoku |   SER |     1
                   |-------|------
Not counted elims  |     0 |    83
Naked Singles      |   0.1 |    41
Hidden Singles     |   0.2 |    57
Naked Single  [1]  |   2.5 |     3
Naked Pair    [2]  |     3 |     5
Naked Triple  [3]  |   3.6 |    11
Hidden Quad   [5]  |   5.4 |     7
Hidden Triple [6]  |     4 |     4
Locked Singles[2]  |   2.8 |     4
XY-Wing       [3]  |   4.1 |     8
                   |-------|------
Eliminated Cand's  |   223 |   223
Sum(SER * Cand's)  | 175.4 | 175.4

Initial Candidates :   223
Maximum SER rating :   5.4 <- Approach
Labour rating      : 175.4 <- Experimental rating
Time needed        : 00:00:00.916

Input:

Code: Select all

.1......582.....3...9.4.......6.8..4.3.12.9.66......2.....8..1...85.....7....2..3

The full solving path:

Hidden Text: Show

Code: Select all

1.1> 5c8=8 Hidden Single in row
1.2> 6c2=8 Hidden Single in row
1.3> 9c7=8 Hidden Single in row
1.4> 3c9=8 Hidden Single in col
1.5> 1c4=8 Hidden Single in box
2.6> 1c7=2 Hidden Single in row
2.7> 3c4=2 Hidden Single in row
 Naked/Hidden Pairs,Triplets,Quads  | (345)c1r135 => (-5)r4c1 (-345)r7c1 (-34)r8c1 | (124569)b7e124589 => (-2456)r7c3.
4.8> 7c3=3 Naked Single
5.9> 4c3=2 Hidden Single in col
5.10> 6c4=3 Hidden Single in col
5.11> 4c7=3 Hidden Single in col
6.12> 4c1=1 Hidden Single in row
6.13> 9c3=1 Hidden Single in col
6.14> 4c2=9 Hidden Single in box
7.15> 3c2=7 Hidden Single in col
8.16> 3c8=6 Naked Single
9.17> 3c7=1 Naked Single
10.18> 6c9=1 Hidden Single in row
 Naked/Hidden Pairs,Triplets,Quads  | (479)r2c479 => (-4)r2c3 (-79)r2c5 (-79)r2c6 | (79)r2c49 => (-7)r2c7 | (4)b3e4 => (-4)r1c8 | (4)c7r2 => (-4)r7c7 (-4)r8c7 | (24679)r8c12789 => (-679)r8c5 (-4679)r8c6.
12.19> 2c7=4 Naked Single
 Naked/Hidden Pairs,Triplets,Quads  | (345)c1r135 => (-45)r7c1 (-4)r8c1 | (79)r2c49 => (-79)r2c5 (-79)r2c6 | (24679)r8c12789 => (-679)r8c5 (-4679)r8c6
Pointing, Claiming  | (7)b8r7 => (-7)r7c7 (-7)r7c9 | (4)c4b8 => (-4)r7c6
Naked/Hidden Pairs,Triplets,Quads  | (29)r7c19 => (-9)r7c4 (-9)r7c6
Pointing, Claiming  | (9)b8r9 => (-9)r9c8
XY-chain [3]  |  (7=5)r6c7 (5=6)r7c7 (6=7)r7c6 => (-7)r6c6
Unique Rectangle (type 1)  | r78,c19 => (-29)r8c9.
19.20> 8c9=7 Naked Single
20.21> 2c9=9 Naked Single
20.22> 7c9=2 Naked Single
20.23> 8c7=6 Naked Single
21.24> 1c8=7 Naked Single
21.25> 2c4=7 Naked Single
21.26> 4c8=5 Naked Single
21.27> 6c7=7 Naked Single
21.28> 7c1=9 Naked Single
21.29> 7c4=4 Naked Single
21.30> 7c7=5 Naked Single
21.31> 8c1=2 Naked Single
21.32> 8c2=4 Naked Single
21.33> 8c8=9 Naked Single
21.34> 9c4=9 Naked Single
21.35> 9c5=6 Naked Single
21.36> 9c8=4 Naked Single
22.37> 4c5=7 Naked Single
22.38> 7c2=6 Naked Single
22.39> 7c6=7 Naked Single
22.40> 9c2=5 Naked Single
23.41> 5c3=7 Hidden Single in row
XY-chain [3]  |  (1=5)r2c5 (5=3)r3c6 (3=1)r8c6 => (-1)r2c6 (-1)r8c5
XY-chain [3]  |  (3=5)r3c6 (5=1)r2c5 (1=3)r8c5 => (-3)r8c6 (-3)r1c5
XY-chain [3]  |  (5=3)r3c6 (3=9)r1c5 (9=5)r6c5 => (-5)r5c6 (-5)r6c6 (-5)r2c5.
25.42> 1c5=9 Naked Single
25.43> 2c5=1 Naked Single
25.44> 5c6=4 Naked Single
25.45> 6c5=5 Naked Single
25.46> 6c6=9 Naked Single
25.47> 8c5=3 Naked Single
25.48> 8c6=1 Naked Single
26.49> 5c1=5 Naked Single
26.50> 6c3=4 Naked Single
27.51> 1c3=6 Naked Single
27.52> 1c6=3 Naked Single
27.53> 2c3=5 Naked Single
27.54> 2c6=6 Naked Single
27.55> 3c1=3 Naked Single
27.56> 3c6=5 Naked Single
28.57> 1c1=4 Naked Single

Can't find the error, if any

[denis_berthier]

My 2 cents... I did this puzzle over and over with SiSeSuSo (and manually) and sometimes I need a Forcing Net and sometimes not

Depending on the order of the rules you apply, it's normal you find different resolution paths. But I don't think you ever "need" any forcing net.

Here's a solution where the hardest steps are very short bivalue-chains (the simplest of AICs).

(solve ".1......582.....3...9.4.......6.8..4.3.12.9.66......2.....8..1...85.....7....2..3")
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin
*** Using CLIPS 6.32-r779
*** Download from: https://github.com/denis-berthier/CSP-Rules-V2.1
***********************************************************************************************
7 singles
Starting non trivial part of solution with the following RESOLUTION STATE:

Code: Select all

   34        1         3467      8         3679      3679      2         4679      5         
   8         2         4567      79        15679     15679     1467      3         179       
   35        567       9         2         4         13567     167       67        8         
   1259      579       1257      6         3579      8         1357      57        4         
   45        3         457       1         2         457       9         8         6         
   6         8         1457      3479      3579      34579     1357      2         17       
   23459     4569      23456     3479      8         34679     4567      1         279       
   12349     469       8         5         13679     134679    467       4679      279       
   7         4569      1456      49        169       2         8         4569      3         

191 candidates, 1119 csp-links and 1119 links. Density = 6.17%

whip[1]: c2n4{r9 .} ==> r9c3 ≠ 4, r7c1 ≠ 4, r7c3 ≠ 4, r8c1 ≠ 4
whip[1]: r6n9{c6 .} ==> r4c5 ≠ 9
finned-x-wing-in-rows: n3{r3 r8}{c1 c6} ==> r7c6 ≠ 3
biv-chain[2]: r5n7{c6 c3} - c2n7{r4 r3} ==> r3c6 ≠ 7
naked-triplets-in-a-column: c1{r1 r3 r5}{n4 n3 n5} ==> r8c1 ≠ 3, r7c1 ≠ 5, r7c1 ≠ 3, r4c1 ≠ 5
singles ==> r7c3 = 3, r4c3 = 2, r6c4 = 3, r4c7 = 3, r4c1 = 1, r4c2 = 9, r3c2 = 7, r3c8 = 6, r3c7 = 1, r6c9 = 1, r9c3 = 1
whip[1]: c4n4{r9 .} ==> r7c6 ≠ 4, r8c6 ≠ 4
naked-pairs-in-a-row: r2{c4 c9}{n7 n9} ==> r2c7 ≠ 7, r2c6 ≠ 9, r2c6 ≠ 7, r2c5 ≠ 9, r2c5 ≠ 7
naked-single ==> r2c7 = 4
hidden-pairs-in-a-block: b8{n1 n3}{r8c5 r8c6} ==> r8c6 ≠ 9, r8c6 ≠ 7, r8c6 ≠ 6, r8c5 ≠ 9, r8c5 ≠ 7, r8c5 ≠ 6
whip[1]: r8n7{c9 .} ==> r7c7 ≠ 7, r7c9 ≠ 7
naked-pairs-in-a-row: r7{c1 c9}{n2 n9} ==> r7c6 ≠ 9, r7c4 ≠ 9
whip[1]: b8n9{r9c5 .} ==> r9c8 ≠ 9
biv-chain-rc[3]: r7c6{n7 n6} - r7c7{n6 n5} - r6c7{n5 n7} ==> r6c6 ≠ 7
biv-chain[3]: c6n9{r1 r6} - r6n4{c6 c3} - r1c3{n4 n6} ==> r1c6 ≠ 6
biv-chain[3]: b7n5{r7c2 r9c2} - r9c8{n5 n4} - c4n4{r9 r7} ==> r7c2 ≠ 4
stte

[Hajime]

Depending on the order of the rules you apply, it's normal you find different resolution paths. But I don't think you ever "need" any forcing net.

I agree, My previous solution was using some XY-chains of length 3.
The next solution is without any method (no naked/hidden subsets, pointing/claiming, etc) except 2 Forcing Nets:

r1c1=3 --> singles only to r9c2=void => (-3)r1c1
r1c8=9 --> singles only to r8c2=void => (-9)r1c8

Void = cell not solved and no candidates left.
These 2 eliminations of candidates will lead to a puzzle that can be solved with singles only.

The full solving path (with the complete forcing nets):

Hidden Text: Show

Code: Select all

1.1> r5c8=8 Hidden Single in row
1.2> r6c2=8 Hidden Single in row
1.3> r9c7=8 Hidden Single in row
1.4> r3c9=8 Hidden Single in col
1.5> r1c4=8 Hidden Single in box
2.6> r1c7=2 Hidden Single in row
2.7> r3c4=2 Hidden Single in row
Forcing Net  |
r1c1=3 -->  r1c1=3 r3c1=5 r5c1=4 r3c6=3 r8c5=3 r7c3=3 r6c4=3 r4c7=3 r6c6=4 r3c7=1 r6c5=9 r4c3=2 r6c9=1 r4c1=1 r4c2=9 r9c3=1 r8c6=1 r9c5=6 r1c5=7 r2c4=9 r2c9=7 r3c8=6 r4c5=5 r4c8=7 r5c6=7 r6c7=5 r7c6=9 r7c9=2 r8c9=9 r9c4=4 r9c8=5 r1c6=6 r2c5=1 r2c6=5 r2c7=4 r3c2=7 r5c3=5 r6c3=7 r7c4=7 r7c7=6 r8c1=2 r8c7=7 r8c8=4 r9c2=void => (-3)r1c1.
4.8> r1c1=4.Naked Single
4.9> r5c1=5.Naked Single
5.10> r3c1=3.Naked Single
6.11> r2c7=4 Hidden Single in row
6.12> r7c3=3 Hidden Single in col
6.13> r6c4=3 Hidden Single in col
6.14> r4c7=3 Hidden Single in col
7.15> r4c3=2 Hidden Single in col
8.16> r4c1=1 Hidden Single in row
8.17> r9c3=1 Hidden Single in col
8.18> r2c3=5 Hidden Single in col
8.19> r1c3=6 Hidden Single in col
8.20> r3c2=7 Hidden Single in box
8.21> r3c6=5 Hidden Single in box
8.22> r4c2=9 Hidden Single in box
9.23> r3c8=6.Naked Single
10.24> r3c7=1.Naked Single
11.25> r6c9=1 Hidden Single in row
.Forcing Net  |
r1c8=9 -->  r1c8=9 r2c9=7 r2c4=9 r9c4=4 r9c8=5 r4c8=7 r6c7=5 r7c4=7 r7c7=6 r8c7=7 r8c8=4 r9c2=6 r9c5=9 r4c5=5 r6c5=7 r8c2=void => (-9)r1c8.
13.26> r1c8=7.Naked Single
13.27> r2c9=9.Naked Single
13.28> r4c8=5.Naked Single
13.29> r6c7=7.Naked Single
13.30> r8c7=6.Naked Single
14.31> r2c4=7.Naked Single
14.32> r4c5=7.Naked Single
14.33> r5c6=4.Naked Single
14.34> r6c3=4.Naked Single
14.35> r6c6=9.Naked Single
14.36> r7c7=5.Naked Single
14.37> r8c2=4.Naked Single
14.38> r8c8=9.Naked Single
14.39> r9c8=4.Naked Single
15.40> r1c6=3.Naked Single
15.41> r5c3=7.Naked Single
15.42> r6c5=5.Naked Single
15.43> r7c2=6.Naked Single
15.44> r7c6=7.Naked Single
15.45> r7c9=2.Naked Single
15.46> r8c1=2.Naked Single
15.47> r8c6=1.Naked Single
15.48> r8c9=7.Naked Single
15.49> r9c2=5.Naked Single
15.50> r9c4=9.Naked Single
15.51> r9c5=6.Naked Single
16.52> r1c5=9.Naked Single
16.53> r2c5=1.Naked Single
16.54> r2c6=6.Naked Single
16.55> r7c1=9.Naked Single
16.56> r7c4=4.Naked Single
16.57> r8c5=3.Naked Single

Helàs, no one-step solution