The New Sudoku Players' Forum

[Sudoku123456789]

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Please explane solution and give name of technique.

Hints were used to validate earlier used techniques.

I'm having the idea i'm really close...

Any tips for in the future?

[JC Van Hay]

1. Only eventual "~fish?" for the digits 7 and 8 => extremely easy puzzle
2. Incomplete application of the Sudoku Rule : a candidate is (placed/excluded) if it (belongs/doesn't belong) to all the solutions either of the same digit or of a unit.
2a. You exclude 8r8c5, but the solutions of the 8s exclude 8r8c5 and 8r7c89. Interpretation : Skyscraper(8C67)
2b. The solutions of C6 exclude (27)r7c6. Interpretation : NP(27)r39c6 or HP(58)r57c6
3. NP(79)r7c39; stte

[Sudoku123456789]

1. Only eventual "~fish?" for the digits 7 and 8 => extremely easy puzzle
2. Incomplete application of the Sudoku Rule : a candidate is (placed/excluded) if it (belongs/doesn't belong) to all the solutions either of the same digit or of a unit.
2a. You exclude 8r8c5, but the solutions of the 8s exclude 8r8c5 and 8r7c89. Interpretation : Skyscraper(8C68)
2b. The solutions of C6 exclude (27)r7c6. Interpretation : NP(27)r39c6 or HP(58)r57c6
3. stte

Thanks again JC!

Unfortunately i missed somethings that were too obvious, such as the naked pair (2b) and the exclution of 8r7c89 (2a).
I know the principle of the skyscraper technique, but i don't see this in 8C68. Shouldn't the 8's be aligned to form a base?
I now removed 8r7c89 with locked candidate 8r7c56.

In addition i also don't understand why this is an exteremly easy puzzle (unfortunately for me not so easy). I don't see why eventually only fishes can be made for 7 and 8.
Could you give an example of where i had an incomplete application of the Sudoku rule?

[Sudoku123456789]

Excuse me for my rookie questions, spending hours daily trying to improve my skillset.

[JC Van Hay]

Sudoku rule : in a solution of the puzzle, a digit is present only once in each unit.
Therefore, in a puzzle, a digit is (placed in/excluded of) a cell if it is (present/absent) in all the solutions of that digit.

Hidden singles; marked locked candidates and marked bilocals (for example : ., -, | if in the box, the row, the column, repectively) are thus first written in the grid.
Now, in order to get a further eventual placement/exclusion, a proper or not subset of the unsolved boxes not containing locked candidates should form a closed loop (Keith's principle), like in the following simplest examples :

Code: Select all

+---------+---------+---------+
|-1  1  . | 1  1  . | .  .  . |
| 1  1  . | 1  .  . | .  .  . |
| .  .  . | .  .  . | .  .  1 |
+---------+---------+---------+
| 1  1  . | 1  1  . | .  .  . |
| 1  .  . | 1  .  . | .  .  . |
| .  .  . | .  .  . | .  .  1 |
+---------+---------+---------+
| .  .  . | .  .  . | .  .  . |
| .  .  . | .  .  . | .  .  . |
| .  .  1 | .  .  1 | .  .  . |
+---------+---------+---------+


XWing(1R24), XWing(1C24), Kite(1R4C4), ER(1R4B2), ER(1C4B4) => -1r1c1
XWing(1R25), XWing(1C25), Kite(1R5C5), ER(1R5B2), ER(1C5B3) => -1r1c1

Code: Select all

+---------+---------+---------+
|-1  1  . | 1  1  . | .  .  . |
| 1  1  . | 1  .  . | .  .  . |
| .  .  . | .  .  . | .  .  1 |
+---------+---------+---------+
| 1  1  . | .  .  . | 1  1  . |
| 1  .  . | .  .  . | 1  .  . |
| .  .  . | .  .  1 | .  .  . |
+---------+---------+---------+
| .  .  . | 1  1  . | 1  1  . |
| .  .  . | 1  .  . | 1  .  . |
| .  .  1 | .  .  . | .  .  . |
+---------+---------+---------+


Swordfish(1R258), Swordfish(1C258), ... => -1r1c1
In such a case, it becomes necessary to determine the common exclusions associated with each set of solutions of the digit from each candidate of a simple constraint (for example : a bilocal, most of the time, or a trilocal covering 2 or 3 boxes). Note however, that a complete and detailed enumeration of the solutions of the digit is not required if the Keith's principle is taken into account during the process. For completeness, it remains then to justify each exclusion by the solutions of the least number of constraints for the digit.


Furthermore, in a solution of the puzzle, the sudoku rule imply that each unit contains a permutation of the 9 digits.
Except for the hidden pairs and obvious ones, the other eventual naked and hidden subsets are easily found by inspection of the 27 units once all the candidates are determined.

In the present puzzle :

8 hidden singles
HP(19)r7c79
6 hidden singles
Locked candidates leading to exclusions : 1R8 , 2B7 or 2C1, 5B4, 6B4 ou 6B7
HP(29)r1c17; r2c1=8

Application of Keith's principle : possible exclusions from the solutions of the 7s, 8s, 9s
No exclusion among the 7s and the 9s.
Skyscraper 8C67 : 8r7c6=8r5c6-8r5c7=8r8c7 -> 8r7c6==8r8c7 => -{8r8c5, 8r7c89}

NP(79)r7c39; stte

Note : the level of a puzzle generally increase most of the time with the number N of digits obeying the Keith's principle. Examples : SE=7.x : N~=4; SE=8.x : N~=5.

[Leren]

The puzzle in line format : ...6..9.2..1..8....6.7.4...73.4..29.....1.....18..9.35...1.2.4....9..6..5.7..6...

Code: Select all

*----------------------------------------------*
| 29 8    4    | 5  3     1     | 29  7    6   |
| 25 57   37   | 6  247   9     | 1   348  348 |
| 6  17   1379 | 8  247  #27    | 29  349  5   |
|--------------+----------------+--------------|
| 8  3    2    | 4  9     6     | 7   5    1   |
| 7  4    56   | 2  1     58    | 689 3689 389 |
| 1  9    56   | 7  58    3     | 4   68   2   |
|--------------+----------------+--------------|
| 4  2567 79   | 19 2578 x58-27 | 3   1689 789 |
| 59 1567 179  | 3  578   4     | 689 2    789 |
| 3  27   8    | 19 6    #27    | 5   149  49  |
*----------------------------------------------*

The naked pair (27) in r39c6 (the cells marked #) removes 27 from r7c6 (marked with an x). A few more easy moves brings the puzzle to the same candidate status shown in your diagram (I think) shown below.

Code: Select all

*--------------------------------------------*
| 29 8    4    | 5  3     1  | 29 7     6    |
| 25 57   37   | 6  247   9  | 1  348   348  |
| 6  17   1379 | 8  247   27 | 29 34    5    |
|--------------+-------------+---------------|
| 8  3    2    | 4  9     6  | 7  5     1    |
| 7  4    56   | 2  1    b58 |c68 39    39   |
| 1  9    56   | 7  58    3  | 4  68    2    |
|--------------+-------------+---------------|
| 4  2567 79   | 19 2578 a58 | 3  169-8 79-8 |
| 59 1567 179  | 3  57-8  4  |d68 2     789  |
| 3  27   8    | 19 6     27 | 5  149   49   |
*--------------------------------------------*

The cells marked a-b-c-d form a Skyscraper. If you are unfamiliar with this move here is a simple explanation:

Suppose cell a was not 8. Then cell b would have to be 8 (only two 8's in Column 6). Then cell c would not be 8. So cell d would have to be 8 (only two 8's in Column 7).

So if cell a is not 8 then cell d is 8. You can reverse this argument, start by assuming cell d is not 8 and work in the opposite direction cells d-c-b-a and you would conclude that cell a would have to be 8.

The result of all this is that you must conclude that at least one of cells a or d must be 8. They might both be 8 but they can't both be not 8.

This means that you can remove 8 from all cells that can see both cells a and d. This occurs in three cells r7c89 and r8c5.

This exposes a naked pair (27) in r7c39, which removes some more candidates in Row 7 and the puzzle then solves easily in singles.

There is a good explanation of Skyscrapers on the Hodoku site here.

The Sudopedia site also has a reasonable explanation here.

Leren

<edit> Fixed broken link to Hodoku, Leren

[Sudoku123456789]

JC, thank you for the extended explanation. I appreciate this a lot.

Keith's principle I now understand, in the basics, thanks to you. Is there any background literature available about this. I searched for it but was not able to find some.
If i may simplify your words: I first look for restraints (bilocals/trilocals etc.) and from there on look for a patterns in the unsolved cells? Where do i draw the line/what is a cut off point? For instance, is 4 possible cells for a candidate still a (usable) restraint?

In your example the 'unsolved' boxes form themselves a square, is Keith's principle still aplied when the distribution would be like: B2349?

The examples you made must be very clear. Still I have some questions... I don't want to be tiresome, but the logic is not that clear to me.

Code: Select all

+---------+---------+---------+
|-1  1  . | 1  1  . | .  .  . |
| 1  1  . | 1  .  . | .  .  . |
| .  .  . | .  .  . | .  .  1 |
+---------+---------+---------+
| 1  1  . | 1  1  . | .  .  . |
| 1  .  . | 1  .  . | .  .  . |
| .  .  . | .  .  . | .  .  1 |
+---------+---------+---------+
| .  .  . | .  .  . | .  .  . |
| .  .  . | .  .  . | .  .  . |
| .  .  1 | .  .  1 | .  .  . |
+---------+---------+---------+


XWing(1R24) -> an additional 1R2C2
XWing(1C24) -> how is an X-wing possible? three ones at C2R124 and 4 ones at C4R1245
Kite(1R4C4) -> possible with 4 candidates in 1 unit? all examples show 2 candidates per string (e.g. http://hodoku.sourceforge.net/en/tech_sdp.php#sk)
ER(1R4B2) -> this 1 is correct, because of strong link R4 => -1r1c1
ER(1C4B4) -> no strong link visible to ERI.


Or is it due to my interpretation of your examples and you meant that those were 'possible' usable techniques?

Code: Select all

+---------+---------+---------+
|-1  1  . | 1  1  . | .  .  . |
| 1  1  . | 1  .  . | .  .  . |
| .  .  . | .  .  . | .  .  1 |
+---------+---------+---------+
| 1  1  . | .  .  . | 1  1  . |
| 1  .  . | .  .  . | 1  .  . |
| .  .  . | .  .  1 | .  .  . |
+---------+---------+---------+
| .  .  . | 1  1  . | 1  1  . |
| .  .  . | 1  .  . | 1  .  . |
| .  .  1 | .  .  . | .  .  . |
+---------+---------+---------+


Swordfish(1R258) --> exceeds number of allowed columns used (4 in total - C1247)
Swordfish(1C258) --> possible, but doesn't this lead to more exclusions than -1R1C1?

In such a case, it becomes necessary to determine the common exclusions associated with each set of solutions of the digit from each candidate of a simple constraint (for example : a bilocal, most of the time, or a trilocal covering 2 or 3 boxes). Note however, that a complete and detailed enumeration of the solutions of the digit is not required if the Keith's principle is taken into account during the process. For completeness, it remains then to justify each exclusion by the solutions of the least number of constraints for the digit.


Furthermore, in a solution of the puzzle, the sudoku rule imply that each unit contains a permutation of the 9 digits.
Except for the hidden pairs and obvious ones, the other eventual naked and hidden subsets are easily found by inspection of the 27 units once all the candidates are determined.

Do you implicate after an extensive enumeration of candidates? This would be in contrast with Keith's principle. I might understand this wrong (I applied the principle several times now), but naked subsets can only be identified after a total enumeration.


Happy to tell you I improved my time on expert substantially! Hard work is giving results.

[Sudoku123456789]

Thank you too Leren,

The puzzle in line format : ...6..9.2..1..8....6.7.4...73.4..29.....1.....18..9.35...1.2.4....9..6..5.7..6...

The cells marked a-b-c-d form a Skyscraper. If you are unfamiliar with this move here is a simple explanation:

What is this line format? Is this notation used for a technique?

Although i was already familiar with the skyscraper technique, thank you anyway.

[Leren]

Sudoku1234567 wrote : What is this line format? Is this notation used for a technique?

Line format is just an efficient way of presenting a puzzle, and is a format used for puzzle input by many computer solvers. It's very useful when you are presenting a list of a large number of puzzles.

The numbers are the clues and the . s are where there is no clue. Some people use 0 instead of .

Leren

[eleven]

There are many ways to find the elimination in JC's examples.
The easiest for me is by x-chain, i.e. following strong links.

Code: Select all

    +---------+---------+---------+
    |-1  1  . | 1 a1  . | .  .  . |
    | 1  1  . | 1  .  . | .  .  . |
    | .  .  . | .  .  . | .  .  1 |
    +---------+---------+---------+
    |c1 c1  . | 1 b1  . | .  .  . |
    |d1  .  . | 1  .  . | .  .  . |
    | .  .  . | .  .  . | .  .  1 |
    +---------+---------+---------+
    | .  .  . | .  .  . | .  .  . |
    | .  .  . | .  .  . | .  .  . |
    | .  .  1 | .  .  1 | .  .  . |
    +---------+---------+---------+

1r1c5=r4c5-r4c12=r5c1 => -1r1c1
This is a kite (or ER or 2 strong links ab,cd). In words:
either r1c5=1
or r4c5=1, then r4c12 is not 1, then r5c1=1
So one of r1c5 and r5c1 must be 1, r1c1 can't be 1.

Code: Select all

    +---------+---------+---------+
    |-1  1  . | 1 a1  . | .  .  . |
    | 1  1  . | 1  .  . | .  .  . |
    | .  .  . | .  .  . | .  .  1 |
    +---------+---------+---------+
    |g1 g1  . | .  .  . |e1 f1  . |
    |h1  .  . | .  .  . |e1  .  . |
    | .  .  . | .  .  1 | .  .  . |
    +---------+---------+---------+
    | .  .  . | 1 b1  . |c1 c1  . |
    | .  .  . | 1  .  . |d1  .  . |
    | .  .  1 | .  .  . | .  .  . |
    +---------+---------+---------+

1r1c5=r7c5-r7c78=r8c7-r45c7=r4c8-r4c12=r5c1 => -1r1c1