The New Sudoku Players' Forum

[Hajime]

This is a Twin-4; 2 vanilla Sudoku's with 4 overlapping boxes

Code: Select all

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

#2//B4/E10
29.31......1..6...3.4......5...6.2.........6.94..5....8...........8..........9..2
.6.2.........6.....5......6.........8..........9..23..3.2....1.....784.2..41...6.


Is this difficult to solve or easy and why?

[urhegyi]

Making use of the rules defined by the overlapping boxes it's easy, without it it's difficult.

[m_b_metcalf]

Is this difficult to solve or easy and why?

I'd guess the SE rating to be in the range 6 to 8:

Code: Select all

  2  9  5  3  1  4  6  7  8         
  7  8  1  5  9  6  3  2  4           
  3  6  4  7  8  2  1  9  5           
  5  3  8  1  6  7  2  4  9  5  3  8 
  1  7  2  9  4  8  5  6  3  2  7  1 
  9  4  6  2  5  3  7  8  1  9  4  6 
  8  1  7  4  2  5  9  3  6  1  8  7 
  6  2  9  8  3  1  4  5  7  6  2  9 
  4  5  3  6  7  9  8  1  2  3  5  4 
           3  8  2  6  9  4  7  1  5
           5  1  6  3  7  8  4  9  2
           7  9  4  1  2  5  8  6  3

Mike

[m_b_metcalf]

Using x-sudokus you can get the overlap area to be empty:

Code: Select all

 . 3 7 . 8 . . 9 .
 8 . . 5 2 . . . .
 . . . 9 . 7 . . .
 . . 4 . . . . . . 4 6 .
 . . 2 . . . . . . . . 2
 . . 8 . . . . . . . . .
 . . . . . . . . . . . .
 . . . . . . . . . . 8 6
 . . . . . . . . . . . .
       . 3 . . 1 . . . .
       . . . . 8 6 3 . .
       4 . . 3 . . . 5 .

 Number of clues  25 

.37.8..9.8..52.......9.7.....4........2........8.................................
......46.........2.........................86..........3..1........863..4..3...5.

Mike

[Hajime]

rules defined by the overlapping boxes

Do you have a link for these methods?

In a next version of SiSeSuSo a new method for overlapping multiple Sudokus is implemented. I don't know the name, will soon describe it.
Without it, the above puzzle needs guessing like forcing chains or nets, indeed SE>6 like Mike said. But with it, it is like pointing/claiming.

[Hajime]

Using x-sudokus you can get the overlap area to be empty

Yes, without x-sudokus (just plain vanilla) I could not find a puzzle with the overlap area to be empty.

[m_b_metcalf]

Yes, without x-sudokus (just plain vanilla) I could not find a puzzle with the overlap area to be empty.

My best result was 3 clues in the overlap region:

Code: Select all

 . . 3 . . . . . 8
 . 9 . . 5 4 . . .
 . 4 8 . 1 . . . .
 . 8 7 . . . . . . . . 9
 . . . . 7 . 3 . . . . .
 . 5 . . . . . . . 2 . .
 . . 4 . . . . . . . . .
 . . . . . . . . . 9 . .
 . . . 2 . . . . . 6 7 .
       . . . . . . . . .
       . . 2 7 . 3 . . .
       . . 9 . 6 2 . . 8

 Number of clues  27 

..3.....8.9..54....48.1.....87..........7.3...5.........4..................2.....
........9.7.3...........2.................9..2.....67............27.3.....9.62..8

Mike

[blue]

Yes, without x-sudokus (just plain vanilla) I could not find a puzzle with the overlap area to be empty.

My best result was 3 clues in the overlap region

Shapes like this, in the overlap region, always contain an unavoidable set.

Code: Select all

+-------+-------+
| . . . | x x x |
| . . . | x x x |
| . . . | x x x |
+-------+-------+
| x x x | x x x |
| x x x | x x x |
| x x x | x x x |
+-------+-------+

You need at least two clues to hit all 4 shapes.
Two clues is possible.

Code: Select all

3 6 2 7 8 4 9 5 1
8 9 4 5 1 3 2 6 7
7 1 5 2 9 6 4 8 3
1 8 9 . . . . . . 9 1 8
2 3 7 . . . . . . 7 3 2
4 5 6 . . 7 . . . 4 6 5
9 2 8 . . . 1 . . 8 2 9
6 4 1 . . . . . . 1 4 6
5 7 3 . . . . . . 5 7 3
      7 9 4 2 8 3 6 5 1
      2 1 6 9 5 7 3 8 4
      5 8 3 4 6 1 2 9 7

362784951894513267715296483189......237......456..7...928...1..641......573......
......918......732..7...465...1..829......146......573794283651216957384583461297

[blue]

In a next version of SiSeSuSo a new method for overlapping multiple Sudokus is implemented. I don't know the name, will soon describe it.
Without it, the above puzzle needs guessing like forcing chains or nets, indeed SE>6 like Mike said. But with it, it is like pointing/claiming.

State and after singles & "normal" locked candidates.

Code: Select all

+-----------------+------------------+------------------------+
| 2    9     58   | 3     1     4    | 56      7      568     |
| 7    58    1    | 59    89    6    | 3459    2      34589   |
| 3    6     4    | 579   789   2    | 1       59     589     |
+-----------------+------------------+------------------------+------------------------+
| 5    378   378  | 1479  6     1378 | 2       3489   3479    | 578      3578   3578   |
| 1    2378  2378 | 479   3479  378  | 345789  6      34579   | 1278     2378   1378   |
| 9    4     6    | 2     5     378  | 378     138    137     | 9        4      6      |
+-----------------+------------------+------------------------+------------------------+
| 8    1257  2579 | 1467  2347  1357 | 345679  13459  1345679 | 12578-6  25789  145789 |
| 46   1257  2579 | 8     2347  1357 | 345679  13459  1345679 | 12567    2579   14579  |
| 4-6  1357  357  | 1467  47    9    | 45678   1458   2       | 3        57     1457   |
+-----------------+------------------+------------------------+------------------------+
                  | 3     789   2    | 4569    59-4   4569    | 578      1      5789   |
                  | 59    1     6    | 359     7      8       | 4        359    2      |
                  | 579   789   4    | 1       2      359     | 578      6      35789  |
                  +------------------+------------------------+------------------------+

I'm guessing that the (3) eliminations that are shown, are the kind that you're talking about.
They (do) reduce the PM to being solvable with singles & "normal" locked candidates.

[Hajime]

Yes blue. That is the idea.
Let AAABBBBBBCCC be a row of the puzzel with AAA only in grid 1 and CCC in grid 2.
BBBBBB is in the overlapping part.

All clues in AAA must be in CCC and visa versa.
And candidates not in AAA can not be in CCC.

Your 3 cells have that characteristic.
Also g2r4c9 <> 4

Has this method a name?

[m_b_metcalf]

Has this method a name?

action-at-a-distance?

Mike

[blue]

Yes blue. That is the idea.
Let AAABBBBBBCCC be a row of the puzzel with AAA only in grid 1 and CCC in grid 2.
BBBBBB is in the overlapping part.

All clues in AAA must be in CCC and visa versa.
And candidates not in AAA can not be in CCC.

Has this method a name?

They seem like (more or less) standard "locked candidate" eliminations to me.
If a candidate doesn't appear in AAA, then it's locked in BBBBBB in the AAABBBBBB row (from grid 1), and in the BBBBBBCCC row (from grid 2), it can be eliminated from CCC.