Superior Variants

For fans of Killer Sudoku, Samurai Sudoku and other variants

Postby tarek » Thu Jul 31, 2008 11:21 pm

Code: Select all
Samurai, Subgrids: Windoku-X
.5...........3.1......8..4...1............6.1..5..1...6..7.....5...........6.....
...91......7.......1.......2.3.........2....7....3...8.....6.8.......9.......8...
...2.................8.....3.........7.............5.4.............5.........9...
...8.......6.......8.......8...3....7....8...3.......5.7.....1...8...3.....652...
....5..........2......7..9....4...........92.4.1.........7.4...........6.78......

Max Technique: Naked Quad

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Postby tarek » Fri Aug 01, 2008 12:15 am

Posted by Jean-Christophe on another website:
Code: Select all
Samurai, Subgrids: Vanilla
5137...........7.5.6.5....2....3.86.2.7..6.......9..7.4....2........9.....5......
..8..1...7...38.........41..9..2...42.6.....9.3.68..........9.....293.........86.
...6........9........3.........2..14..2...5..16..9.........9........4........5...
.23.........837.....9..........49.5.9.....3.71...6..2..34.........41...9...2..8..
......7.....4........7....5.8..3.......8..9.4.31.6....8....9.5.3.2...........1248

Max Technique: X-Wing

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Postby Pat » Fri Aug 01, 2008 7:22 am

tarek wrote:For me a naked subset has to be based in relation to one of the regional constraints (in windoku they are 9 rows 9 columns 9 boxes & 9 windoku regions) but this can be generalized to be as you demostrated

Code: Select all
naked x-subset
is exactly x number of different candidates
in x number of cells
that can ALL SEE each other

eliminate similar candidates from cells seen by all x cells


These to me are a special form of xy-ring or ALS-ring



  • where these cells are all in the same unit,
    yes.
  • where they see each other
    without all of them being in the same unit,
    how to you justify the exclusions??
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Postby tarek » Fri Aug 01, 2008 7:46 am

Pat wrote:[*]where they see each other
without all of them being in the same unit,
how to you justify the exclusions??
Naked subsets are actually not bound by unit constraint.

if 3 cells that see each other have only 3 candidates, then these 3 candidates must be in these 3 cells, therfore the cells that can see all of these 3 cells cannot house these candidates.

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Postby Jean-Christophe » Fri Aug 01, 2008 10:06 am

tarek wrote:
Pat wrote:[*]where they see each other
without all of them being in the same unit,
how to you justify the exclusions??
Naked subsets are actually not bound by unit constraint.

if 3 cells that see each other have only 3 candidates, then these 3 candidates must be in these 3 cells, therfore the cells that can see all of these 3 cells cannot house these candidates.

tarek

For me these are generalizations of naked subsets. See also the user guide for my soft JSudoku

Here is a windoku which requires such a generalized naked triple:
Code: Select all
...7.3....6.5.......3...7..41......2.........8......47..8...5.......2.3....4.9...

+----------------------+----------------------+----------------------+
| 129    8      129    | 7      1249   3      | 46     56     15     |
| 179    6      2479   | 5      *19    8      | *49    2-9    3      |
| 5      249    3      | 29     6      *14    | 7      129    8      |
+----------------------+----------------------+----------------------+
| 4      1      79     | 8      79     56     | 3      56     2      |
| 23679  239    269    | 239    2479   45     | 1      8      59     |
| 8      2359   259    | 1239   1239   16     | 69     4      7      |
+----------------------+----------------------+----------------------+
| 1269   249    8      | 136    13     7      | 5      19     1469   |
| 169    7      49     | 16     5      2      | 8      3      1469   |
| 136    35     156    | 4      8      9      | 2      7      16     |
+----------------------+----------------------+----------------------+

r2c57, r3c6 forms a generalized naked Triplet on {149} -> r2c8 <> 9 = 2

It can also be viewed as a generalized XY-Wing:
XY-Wing on 9 with pivot r3c6, pincers r2c5 & r2c7 -> r2c138 <> 9
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re: new "naked" beast

Postby Pat » Sun Aug 03, 2008 4:54 am

tarek wrote:Naked subsets are actually not bound by unit constraint.

if j cells which see each other
have only j candidates,
then these j candidates
must be in these j cells;
therefore,
a cell which sees all of these j cells
cannot house these candidates.


yes, tarek, and thanks
    my double-questionmark sounds too strong -- sorry!!
this is what i should've said --

the term "naked" subset
refers to cells which are a subset of some set (unit, sector);
your new "naked" beast
it is no longer a subset,
and we should find a new term to reflect this;
also, it would be good to have a few words by way of proof.


sorry i was too rushed to phrase it properly -- anyway thanks again for your response -- and if you can suggest a new term that would be great!
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Postby tarek » Tue Aug 05, 2008 7:44 am

Ah, No worries Pat.

Well a "Locked Set" seems to be the one that we are after.

the use of "SUB" is what seems to cause all of this confusion.

The genarlized form of naked triple that JC showed is better because the set is not housed entirely within one constraint as my example showed.

In vanilla Sudokus These "Fruitful" Locked sets will always be a a naked -subset with their eliminations always within that bigger set.

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Postby tarek » Wed Aug 06, 2008 5:38 am

Code: Select all
Samurai, Subgrids: All Windoku X
.....6.8...9.......7.....1.....3...8...6.....9.....6.......2...3.5.........3.....
...18......8....1..9.....3.5.......8...9.2...2.......6......2........5......27...
..............5........4...........2.......5..73...................6.......9.....
...3.1.....8.......1.......1...8....6.......3....7...4......45..71.........9.5...
...2.6.........9.........7.7.......3.....7...3...2.....1....6....2.........7.....
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Postby tarek » Wed Aug 06, 2008 5:45 am

Code: Select all
2 Girandolas:
...9.7.4...1.....7.5.4.3...8.7...9.2.........6.4...1.8...1.6.3.1.....7...2.3.9...
.7.....9.6.5...8.2...5.2.......2.......1.8...8.6...2.4...9.5....8.....5..3.....4.

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Postby HATMAN » Fri Aug 08, 2008 8:22 pm

Tarek just to position you is "The Midlands" the Black Country or the urban sprawl further to the east (note two of my sisters live in that sort of western area)
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Postby tarek » Sat Aug 16, 2008 6:19 am

HATMAN wrote:Is "The Midlands" the Black Country or the urban sprawl further to the east ?
West Midlands reach the Welsh border, while the East Midlands include Lincolnshire. The Urban Sprawl in the middle of that to me deosn't include Birmingham (Which is west) but includes Leicester, Derby & Possibly Nottingham.

BTW, When was the last time you read your private messages:D:?:

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Postby udosuk » Sun Aug 17, 2008 5:10 am

tarek wrote:BTW, When was the last time you read your private messages:D:?:

So I ain't the only one having troubles trying to communicate with him privately...:)
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Postby evert » Tue Oct 28, 2008 12:38 pm

I'm having some difficulty with defining 'fish' in the sudoku variant context. "Rows" and "Columns" should not appear in the definition anymore.
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Postby Glyn » Tue Oct 28, 2008 2:16 pm

evert It is probably best to start thinking of the 'fish' in terms of constraint groups of which Rows and Columns are special cases. Incorporating Boxes is common for vanilla sudoku for Mutant- and Frankenfish, but with the variants a whole host of new groupings comes into play.
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Postby evert » Wed Oct 29, 2008 12:33 pm

I think a definition of Fish could be as follows:

1. There are n different groups g(i) (i = 1..n).
2. A certain digit k has n different possible placements in each of the groups g(i).
3. None of these cells occur in more then one of the groups g(i).
4. There are also n different groups h(j) (j = 1..n).
5. Each group h(j) contains exactly one of the cells from each group g(i) where digit k can be placed.
6. Each placement for k in one of the groups g(i) occurs in exactly one of the groups h(j).

In this situation: k can be excluded from every cell in a group h(j), that does not occur in any of the groups g(i).

I wonder if this definition is both minimal and sufficient.
Sufficient in the sense that the exclusion of k is justified.
Minimal in the sense that all conditions 1 to 6 are necessary - otherwise the exclusion of k is not justified.
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