Superior Variants

For fans of Killer Sudoku, Samurai Sudoku and other variants

Superior Variants

Postby tarek » Tue Jul 22, 2008 10:32 am

I'm thinking of a thread similar to the corresponding vanilla one

This one however is all about variants.

If you think that it is a good idea then we can probably start posting stuff in this thread straight away.

If it is going to be left for me to check the validity of each, then some limitations would need to be present:

techniques used to solve:
Singles (hidden naked)
Subsets(hidden naked)
1-fish (sector sector intersections)
2-fish (aka x-wing)

fish can be of any configuration (basic, franken,mutant)
Fins anyone ???

techniques needed to solve:
3-subset (hidden or naked) OR
2-fish (aka x-wing)

Single puzzle constarints:
Latin square variants (possibly toroidals, NO jigsaw)
Vanilla variants (too many but should be the commonest ones, No Chess variants)

Overlapping puzzles:
currently will be limited to Samurai
but will try to add support for (gattai-5 windmill, clueless special, sumo, 3-D)

No other variants (shape & aritmatic constraints)

I would appreciate your thoughts before committing some time to tweak the solver.

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Postby Glyn » Tue Jul 22, 2008 12:20 pm

tarek

What a good idea the variant techniques do get overlooked. Things such as the additional fish which appear due to the action of extra constraints such as diagonal and NRC.

On the subject of Clueless since Ruud's retirement some players have resorted to producing their own and the resulting difficulty level has increased. Puzzles are now being posted with chains/ALS that bridge grids, they are more difficult to spot than in Samurai. I am wondering whether some humongous fish may be swimming in those waters as well. These more intransigent puzzles cannot be solve by sequentially visiting grids even using forcing.

The two main logical solvers for these in the public have so far failed to defeat some of the more difficult problems without Brute Force. One already has implemented some inter-grid chains.
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Postby tarek » Tue Jul 22, 2008 4:03 pm

Thanks Glyn,

I agree that some of the overlapping puzzles can be more daunting if more difficult techniques are used (cluless special, 3-D). To me
, they are like sitting in the front row in a tennis match. You end up with a neck-ache. Restricting stuff to a smaller number of overlapping puzzles is better.

from a programmers point of view, a cell can be seen as a cell in grid "A" and act accordingly, then as a cell in grid "B" and act accordingly. It can also be seen as one cell the can see sectors in more than one grid.... It would be interesting to see fish that use cover sectors from more than one grid.

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Postby Glyn » Tue Jul 22, 2008 5:19 pm

In principle once the method of dealing with inter-grid chains is accomplished for Samurai it should be easily extended to larger assemblies of grids. For the non-computer solver the sheer range of potential chains and other structures, both in variety and 'geographically' over the whole puzzle, is daunting.

Borge over at the SudokuSolver forum sets weekly Samurai, Clueless Special and Clueless Explosions. Usually several sets of givens are produced, all with the same solution, but requiring different levels of complexity in the required solving techniques. It is quite interesting to speculate on the number of backdoors required, some guesses can be made from looking at the givens for the simpler grades, but it can potentially be much greater than a single grid puzzle.

At present I consider the gold standard of difficulty to be an X-Samurai, produced by Ruud, which he called Ronin. There is no easy way of comparing it to a vanilla SE rating.
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Postby udosuk » Wed Jul 23, 2008 2:17 am

Great idea tarek!:)

I wonder if by "vanilla variants" you include NC (Non-Consecutive), which isn't arithmetical IMO. Also the "touchless/anti-king" property is marginally a "chess variant" but should often make interesting puzzles.

The commonly accepted "vanilla variants" I know of are X, Windoku, DG etc. Any more?
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Postby tarek » Wed Jul 23, 2008 6:50 am

The Single grid variants that my solver supports are any combination odf the following:

1. Latain square
2. 3x3 boxes (with Latin square you get the Vanilla)
3. DG
4. Diamonds
5. Diagonals (X)
6. Asterisk
7. Centre dot
8. girandola
9. DG diagonals
8. Windoku
9. Windoku2
9. toroidal (1 type)

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Postby Pat » Wed Jul 23, 2008 8:40 am

hey tarek, this sounds like a super-project --
how about breaking it down into smaller pieces?
    i'd like to encourage you to start a separate Topic on "superior" plain Samurai,
    plus a separate Topic on "superior" SuDoku-X,
    etc
    -- while the present Topic could continue as the framework for this super-project
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Postby tarek » Wed Jul 23, 2008 10:37 am

Thanks Pat,

My concern is that there would be too many subthreads.

We can always post stuff here then filter out if needed to seperate threads.

I could start validating stuff & posting hopefully by Monday.

Al are welcome to start posting stuff here.

Minimality & symmetry for the time being are not an issue.

udosuk,

NC & chess moves follow the same programing logic. I'm not against any of this. I'm restricted by validating only what my solver can manage.

with time, I'm sure that there will be room to increase the variety of constraints & overlapping puzzle configuartion.

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Postby tarek » Mon Jul 28, 2008 6:14 am

Unfortuantely,

Posting & reviewing puzzles are on-hold for some problems beyond my control,

Hopefully within the next 7 days this project will be up and running,

:(

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Postby Pat » Tue Jul 29, 2008 9:41 am

tarek wrote:
on-hold for some problems beyond my control



i assume one of the problems beyond your control is,
that your programming effort cannot exceed 36 hours per day---
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Postby tarek » Tue Jul 29, 2008 12:04 pm

Pat wrote:i assume one of the problems beyond your control is,
that your programming effort cannot exceed 36 hours per day---

I tried to work on it in the past few days, sleep deprivation is not the proper way to start a working week.

things hopefully will come through this week.

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Postby tarek » Thu Jul 31, 2008 6:13 am

Working on these superiors, I was delighted to know that subsets in variants can be more lethal....

knowledge of the hidden constraints in Windoku will lead to this
Code: Select all
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .
-------+-------+------
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .
-------+-------+------
 . . . | . . * | * * X
 * . . | . * . | X X *
 . . . | . . . | * * *
naked triple in box 9 ==> X
elimination cells  ==> *

The idea is that the potential elimination cells are those that can be SEEN by all the naked subset cells

as we have the 4th window r678c678 & the hidden constraint r678c159 then the visual field extends to more than box 9 (which is the case in vanilla)

very nice:D

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Postby Jean-Christophe » Thu Jul 31, 2008 8:43 am

Next step, harder to detect. Also taking Windoku as an example
Code: Select all
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .
-------+-------+------
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .
-------+-------+------
 . . . | . . X | * * X
 . . . | . * . | X * .
 . . . | . . . | . . .
naked triple ==> X
elimination cells  ==> *

The idea is that each cell forming the naked subset can see (is a buddy/peer of) all other naked subset cells
Here each of the 3 cells 'X' can see the other 2, either through r7, b9 or window. The victims '*' can see all the 3 cells 'X'.
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Postby tarek » Thu Jul 31, 2008 11:02 am

Jean-Christophe wrote:The idea is that each cell forming the naked subset can see (is a buddy/peer of) all other naked subset cells
Here each of the 3 cells 'X' can see the other 2, either through r7, b9 or window. The victims '*' can see all the 3 cells 'X'.
This is much tougher to detect JC, but still a very interesting point.

For me a naked subset has to be based in relation to one ofthe 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

very interesting.

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Postby tarek » Thu Jul 31, 2008 7:07 pm

I tracked down that example. here it is with my solvers solution for demonstration purposes.

This puzzle is a Windoku-X & is obviously not minimal:(
Code: Select all
Windoku-X
.4.3....2.274......9..2.4..4.3.7.2..7.9..2...2.6.....7138...72.9742..1..562713...
 . 4 . | 3 . . | . . 2 
 . 2 7 | 4 . . | . . . 
 . 9 . | . 2 . | 4 . . 
-------+-------+------
 4 . 3 | . 7 . | 2 . . 
 7 . 9 | . . 2 | . . . 
 2 . 6 | . . . | . . 7 
-------+-------+------
 1 3 8 | . . . | 7 2 . 
 9 7 4 | 2 . . | 1 . . 
 5 6 2 | 7 1 3 | . . . 
.
.
.
8 forms an intersection in w5/r5
[r5c789]<>8
1 forms an intersection in d\/w1
[r3c4][r4c2]<>1
3 forms an intersection in w2/b3
[r23c9]<>3
8 forms an intersection in b8/r8
[r8c89]<>8
8 forms an intersection in w8/c5
[r12c5]<>8
8 forms an intersection in w9/d\
[r4c4][r6c6]<>8
9 forms an intersection in c5/b2
[r12c6]<>9
1 forms an intersection in b2/c6
[r4c6]<>1
4 forms an intersection in b5/r6
[r6c8]<>4
4 forms an intersection in b8/r7
[r7c9]<>4
49 is a hidden 2-subset in d\
[r6c6]<>5 [r9c9]<>8
8 in r1c1 is a hidden single in more than one sector
[r1c678][r23c1]<>8
6 forms an intersection in c1/w7
[r2c59][r34c9]<>6
*--------------------------------------------------------------------------*
| 8       4       15     | 3       69      1567   | 569     15679   2      |
| 36      2       7      | 4       59      1568   | 35689   1369    1589   |
| 36      9       15     | 568     2       15678  | 4       135678  158    |
|------------------------+------------------------+------------------------|
| 4       58      3      | 156     7       69     | 2       15689   1589   |
| 7       158     9      | 158     36      2      | 56      1456    346    |
| 2       15      6      | 19      3458    49     | 3589    3589    7      |
|------------------------+------------------------+------------------------|
| 1       3       8      | 59      456     4569   | 7       2      *56     |
| 9       7       4      | 2      -5-68    568    | 1      *356    *356    |
| 5       6       2      | 7       1       3      | 89      489     49     |
*--------------------------------------------------------------------------*
356 is a naked 3-subset in b9
[r8c5]<>5<>6
8 in r8c5 is a Naked single
[r6c5][r8c6]<>8
8 in r5c4 is a hidden single for b5
[r3c4][r5c2]<>8
8 in r4c2 is a hidden single in more than one sector
[r4c89]<>8
8 forms an intersection in c9/b3
[r2c7][r3c8]<>8
178 is a hidden 3-subset in c6
[r1c6]<>5<>6 [r2c6]<>5<>6 [r3c6]<>5<>6
5 forms an intersection in c6/b8
[r7c45]<>5
.
.
.
845391672627458391391627458483576219719832546256149837138964725974285163562713984
 8 4 5 | 3 9 1 | 6 7 2 
 6 2 7 | 4 5 8 | 3 9 1 
 3 9 1 | 6 2 7 | 4 5 8 
-------+-------+------
 4 8 3 | 5 7 6 | 2 1 9 
 7 1 9 | 8 3 2 | 5 4 6 
 2 5 6 | 1 4 9 | 8 3 7 
-------+-------+------
 1 3 8 | 9 6 4 | 7 2 5 
 9 7 4 | 2 8 5 | 1 6 3 
 5 6 2 | 7 1 3 | 9 8 4


I can now verify any Samurai puzzle for uniqueness & any superior samurai according to the above criteria, I will try to track down these puzzles from the internet & as support for more overlapping variants increases, more puzzles can be verified.

Any suggestion for overlapping puzzles is appreciated.

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