A Similar Variant ?

For fans of Killer Sudoku, Samurai Sudoku and other variants

Postby tarek » Thu Jun 19, 2008 3:30 am

double diamond x 12 clues
Code: Select all
. 1 .|. . .|. 2 .
8 . .|4 . .|. . 9
. . .|. . .|. . .
-----+-----+-----
. . .|. . .|. 3 .
. . .|. . .|. . .
. 5 .|. . .|. . .
-----+-----+-----
. . .|. . .|. . .
1 . .|. . 8|. . 7
. 2 .|. . .|. 1 .


remove r1c2 to get the minimal 11-cluer
Code: Select all
. . .|. . .|. 2 .
8 . .|4 . .|. . 9
. . .|. . .|. . .
-----+-----+-----
. . .|. . .|. 3 .
. . .|. . .|. . .
. 5 .|. . .|. . .
-----+-----+-----
. . .|. . .|. . .
1 . .|. . 8|. . 7
. 2 .|. . .|. 1 .


a 14 clue solvable DG, DG diagonals,double diamonds, X
Code: Select all
7 8 .|. . .|. 1 2
2 . .|. . .|. . 5
. . 3|. . .|. . .
-----+-----+-----
. . .|. . .|. . .
. . .|. . .|. . .
. . .|. . .|. . .
-----+-----+-----
. . .|. . .|4 . .
3 . .|. . .|. . 6
6 7 .|. . .|. 5 1


For the solution, Triple click below to see what I wrote:7 is a given clue in r1c1
[r1c34567][r2c234][r3c127][r4c1247][r5c159][r6c168][r7c134][r8c68][r9c5]<>7
8 is a given clue in r1c2
[r1c34567][r2c23][r3c12][r4c258][r5678c2][r7c58]<>8
1 is a given clue in r1c8
[r1c34567][r2c78][r3c789][r4c258][r5678c8][r7c25]<>1
2 is a given clue in r1c9
[r1c34567][r2c678][r3c789][r4c3689][r5c159][r6c249][r7c369][r8c24][r9c5]<>2
2 is a given clue in r2c1
[r2c2345][r3c12][r467c1][r5c47][r8c7]<>2
5 is a given clue in r2c9
[r123c7][r2c234568][r3c89][r4567c9][r58c36]<>5
3 is a given clue in r3c3
[r12456789c3][r2c26][r3c12456789][r48c48][r5c57][r6c269][r7c5][r9c6]<>3
4 is a given clue in r7c7
[r1c47][r26c267][r3c57][r4c1478][r5c357][r7c12345689][r8c478][r9c7]<>4
3 is a given clue in r8c1
[r2c47][r4567c1][r5c4][r78c2][r8c567]<>3
6 is a given clue in r8c9
[r25c36][r34567c9][r78c8][r8c234567][r9c7]<>6
6 is a given clue in r9c1
[r159c5][r24c8][r3c147][r4c16][r567c1][r6c247][r7c23][r9c346]<>6
7 is a given clue in r9c2
[r3c58][r5678c2][r6c5][r89c3][r9c467]<>7
5 is a given clue in r9c8
[r36c25][r45678c8][r89c7][r9c3456]<>5
1 is a given clue in r9c9
[r2c24][r3689c6][r4c49][r5c159][r67c39][r89c7][r9c345]<>1
3 is locked in DG6/r5
[r5c28]<>3
3 in r4c2 is a hidden single in more than one sector
[r14c5][r4c679][r67c8]<>3
3 in r2c8 is a hidden single for c8
[r1c7][r2c5][r6c4]<>3
4 is locked in b3/r3
[r3c1246]<>4
4 is locked in b1/c3
[r4689c3]<>4
4 in r8c2 is a hidden single for b7
[r28c5][r48c6][r5c28][r6c4]<>4
5 is locked in "\" diagonal/b5
[r4c56][r56c4]<>5
1 is locked in "/" diagonal/b5
[r5c46][r6c5]<>1
5 is locked in b7/r7
[r7c456]<>5
6 is locked in DG2/c5
[r236c5]<>6
7 is locked in "/" diagonal/b5
[r4c5][r5c46]<>7
4 is locked in DG2/c5
[r69c5]<>4
3 is locked in DG1/c4
[r9c4]<>3
5 is locked in "/" diagonal/DG inner diagonal
[r5c7]<>5
46 is a hidden 2-subset in "\" diamond
[r2c4]<>8<>9 [r6c8]<>2<>8<>9
2 in r8c6 is a hidden single for "\" diamond
[r3569c6][r58c3][r7c45][r8c58][r9c4]<>2
2 in r4c4 is a hidden single for "\" diagonal
[r3c4][r4c57][r6c5]<>2
2 in r3c5 is a hidden single in more than one sector
9 is locked in "\" diamond/DG inner diagonal
[r5c37][r7c5]<>9
8 is locked in "\" diamond/"/" diagonal
[r4c6][r6c4]<>8
8 is locked in "/" diagonal/DG inner diagonal
[r5c37]<>8
9 is locked in "\" diamond/"/" diagonal
[r4c6][r6c4]<>9
1 is locked in DG inner diagonal/r5
[r5c2]<>1
23 is a hidden 2-subset in c7
[r6c7]<>1<>5<>7<>8<>9 [r9c7]<>8<>9
5 in r4c7 is a hidden single in more than one sector
[r1c4][r4c13][r7c1]<>5
1 in r5c7 is a hidden single in more than one sector
[r5c3][r8c4]<>1
6 in r7c5 is a hidden single for DG inner diagonal
[r4c5][r7c46]<>6
7 in r5c3 is a hidden and naked single
[r2c6][r46c3][r5c8]<>7
6 in r4c3 is a hidden single for r4
[r1c36][r5c2][r6c3]<>6
1 is locked in DG3/c6
[r2c6]<>1
1 in r6c2 is a hidden single for "/" diamond
[r3c2][r46c1][r6c4]<>1
1 in r4c6 is a hidden single in more than one sector
[r7c6]<>1
7 in r6c4 is a hidden and naked single
[r38c4][r6c9]<>7
7 in r4c8 is a hidden single for "/" diamond
[r4c9][r7c8]<>7
6 is locked in b6/c8
[r3c8]<>6
17 is a hidden 2-subset in c5
[r2c5]<>8<>9 [r8c5]<>5<>8<>9
5 in r8c4 is a hidden single in more than one sector
[r3c4][r5c15]<>5
5 in r1c5 is a hidden single in more than one sector
[r1c36][r3c6][r7c2]<>5
5 in r3c1 is a hidden single in more than one sector
[r6c1]<>5
1 in r3c4 is a hidden single in more than one sector
[r2c5][r7c4]<>1
1 in r2c3 is a hidden single in more than one sector
[r8c3]<>1
4 in r1c3 is a hidden single in more than one sector
[r1c6][r4c9]<>4
4 in r2c4 is a hidden single in more than one sector
[r5c14][r6c8][r9c4]<>4
6 in r6c8 is a hidden and naked single
[r3c2][r5c8][r6c6]<>6
6 in r2c2 is a hidden single in more than one sector
[r2c7]<>6
9 in r3c2 is the last digit to fill the sector
[r3c6789][r57c2][r69c5]<>9
6 in r1c7 is a hidden single in more than one sector
[r1c4]<>6
6 in r3c6 is a hidden single in more than one sector
r5c4 has the last 6 uncovered
7 in r2c5 is a hidden and naked single
[r2c7][r8c5]<>7
r7c1 has the last 1 uncovered
1 in r8c5 is a hidden and naked single
4 in r3c8 is a hidden single in more than one sector
[r3c9]<>4
7 in r3c9 is a hidden single in more than one sector
[r7c9]<>7
8 in r3c7 is the last digit to fill the sector
[r28c7][r5c5][r6c1][r7c3][r9c4]<>8
9 in r2c7 is the last digit to fill the sector
[r2c6][r5c1][r8c7]<>9
8 in r2c6 is the last digit to fill the sector
[r5c69][r679c6][r8c3]<>8
9 in r5c5 is the last digit to fill the sector
[r4c5][r5c689][r6c6][r7c3][r8c8]<>9
5 in r7c3 is the last digit to fill the sector
[r6c3]<>5
r5c2 has the last 5 uncovered
2 in r7c2 is the last digit to fill the sector
[r7c8][r9c3]<>2
r7c6 has the last 7 uncovered
4 in r4c5 is a hidden and naked single
[r5c6]<>4
9 in r7c8 is the last digit to fill the sector
[r7c49]<>9
8 in r5c1 is a hidden and naked single
[r4c1][r5c8][r6c3][r9c5]<>8
7 in r8c7 is the last digit to fill the sector
2 in r5c8 is a hidden and naked single
[r6c7]<>2
8 in r8c8 is the last digit to fill the sector
[r7c9]<>8
5 in r6c6 is the last digit to fill the sector
9 in r8c3 is the last digit to fill the sector
[r69c3]<>9
8 in r9c3 is the last digit to fill the sector
[r6c9]<>8
2 in r6c3 is the last digit to fill the sector
r9c7 has the last 2 uncovered
3 in r6c7 is the last digit to fill the sector
[r5c9][r6c5]<>3
3 in r7c9 is the last digit to fill the sector
[r1c6][r7c4]<>3
8 in r7c4 is the last digit to fill the sector
r1c4 has the last 3 uncovered
9 in r1c6 is the last digit to fill the sector
[r4c9][r9c6]<>9
9 in r4c1 is the last digit to fill the sector
[r6c1]<>9
8 in r4c9 is the last digit to fill the sector
4 in r6c1 is the last digit to fill the sector
[r6c9]<>4
9 in r9c4 is the last digit to fill the sector
3 in r5c6 is a hidden and naked single
4 in r5c9 is the last digit to fill the sector
8 in r6c5 is the last digit to fill the sector
9 in r6c9 is the last digit to fill the sector
3 in r9c5 is the last digit to fill the sector
4 in r9c6 is the last digit to fill the sector
Puzzle Solved
7 8 4|3 5 9|6 1 2
2 6 1|4 7 8|9 3 5
5 9 3|1 2 6|8 4 7
-----+-----+-----
9 3 6|2 4 1|5 7 8
8 5 7|6 9 3|1 2 4
4 1 2|7 8 5|3 6 9
-----+-----+-----
1 2 5|8 6 7|4 9 3
3 4 9|5 1 2|7 8 6
6 7 8|9 3 4|2 5 1

Extreme 10 clue DG, DG diagonals,double diamonds, X (can be reduced to 9 clues)
Code: Select all
. 4 .|. . .|. 1 .
. . .|. . .|. . 9
. . .|. 6 .|. . .
-----+-----+-----
. . .|. . .|. . .
. . 4|. . .|2 . .
. . .|. . .|. . .
-----+-----+-----
. . .|. 3 .|. . .
9 . .|. . .|. . .
. 7 .|. . .|. 8 .

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

6 . .|. . .|. . 2
. . .|. . .|. . .
. . .|. . .|. . 5
-----+-----+-----
. . .|. 1 .|. . .
. . .|3 . 8|. . .
. . .|. 6 .|. . .
-----+-----+-----
9 . .|. . .|. . .
. . .|. . .|. . .
4 . .|. . .|. . 1
tarek
Last edited by tarek on Wed Jun 18, 2008 11:42 pm, edited 1 time in total.
User avatar
tarek
 
Posts: 2612
Joined: 05 January 2006

Postby udosuk » Thu Jun 19, 2008 3:42 am

tarek wrote:Here is a double diamond X
Code: Select all
6 . 8|. 7 .|2 . 3
. . .|. . .|. . .
2 . .|. . .|. . 4
-----+-----+-----
. . .|7 . 5|. . .
1 . .|. . .|. . .
. . .|6 . 1|. . .
-----+-----+-----
7 . .|. . .|. . 5
. . .|. . .|. . .
4 . 3|. . .|6 . 2
mild advanced moves needed

After basic moves (singles, subsets, locked candidates):
Code: Select all
+----------------------+----------------------+----------------------+
| 6      1      8      | 459    7     *49     | 2     *59     3      |
| 39     4      7      | 35     2      6      | 1589   89     189    |
| 2      39     5      | 389    1      389    | 7      6      4      |
+----------------------+----------------------+----------------------+
| 389    389    469    | 7      3489   5      | 13489  2      1689   |
| 1      35689  469    | 23489  89     23489  | 345    7      689    |
| 3589   7      2      | 6      3489   1      | 34589 *45     89     |
+----------------------+----------------------+----------------------+
| 7      689    1      | 23489  346    23489  | 89     489    5      |
| 589    2      69     | 1      45689 -489    | 489    3      7      |
| 4      589    3      | 89     589    7      | 6      1      2      |
+----------------------+----------------------+----------------------+

XY-Wing: r1c8 from {59}
If r1c8=5 => r6c8=4 => r8c6 can't be 4 (leading diamond)
If r1c8=9 => r1c6=4 => r8c6 can't be 4
Therefore r8c6 can't be 4.

Then r8c6 forms a naked pair with r5c5 (leading diamond), solving the puzzle.

coloin wrote:All MC grid isomorphs, I suspected this...

From my study I noticed that a lot of grids with a heavy amount of constraints are bound to be MC isomorphs (if you disregard their extra constraints and treat them as normal vanilla grids). That NNC grid is also one of them because if you notice carefully all mini-rows and mini-columns are formed by similar sets of digits. There are duplicating 3x3 boxes in that grid too.:idea:

I don't think the Double Diamond constraint itself has anything to do with being MC isomorphs. For evidence, just use tarek's puzzle above and I don't think you can normalise it into an MC grid.
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby coloin » Thu Jun 19, 2008 11:25 am

Indeed the double diamond grids are not all the MC isomorphs.

You could say that tarek has been working wonders:!:

from http://www.headington.org.uk/adverts/drinks_alcoholic.htm

Code: Select all
Double Diamond (1): 1950s
Amber bright, plenty of body!
Double Diamond — the beer the men drink!

Double Diamond (2): 1968
A Double Diamond works wonders,
Works wonders, works wonders,
A Double Diamond works wonders,
So drink one today!

[Tune: “There’s a hole in my bucket “]

Double Diamond (3)
I'm only here for the beer: it’s Double Diamond


C
coloin
 
Posts: 1633
Joined: 05 May 2005

Postby tarek » Sat Jun 21, 2008 10:48 am

Diamonds have always been desirable objects, just like beer:D

here is an 11 clue double diamond x. It is difficult enough to cross the border into the extreme. Best to be kept as a machine excercise or as a very extreme challenge for enthusiasts (great solution for the previous one udosuk)
Code: Select all
DDX002
...7.................9..8........3.6....2....7.1........3..5.................1...
. . .|7 . .|. . .
. . .|. . .|. . .
. . .|9 . .|8 . .
-----+-----+-----
. . .|. . .|3 . 6
. . .|. 2 .|. . .
7 . 1|. . .|. . .
-----+-----+-----
. . 3|. . 5|. . .
. . .|. . .|. . .
. . .|. . 1|. . .

Image

tarek
User avatar
tarek
 
Posts: 2612
Joined: 05 January 2006

Postby tarek » Fri Jul 11, 2008 5:12 pm

With a short run of the program, here are some DG ,DG diagonals, Diamonds, X puzzles with the lowest number of clues that displayed symmetry, the solution grids are also included in case somebody has some use for them:D .

Code: Select all
Minimal & Symmetric "DG ,DG diagonals, Diamonds, X" Puzzles

8 clues:

000000000000000000002000800700000000040000030000000001005000600000000000000000000
 . . . | . . . | . . . 
 . . . | . . . | . . . 
 . . 2 | . . . | 8 . . 
-------+-------+------
 7 . . | . . . | . . . 
 . 4 . | . . . | . 3 . 
 . . . | . . . | . . 1 
-------+-------+------
 . . 5 | . . . | 6 . . 
 . . . | . . . | . . . 
 . . . | . . . | . . . 

394862157678154923512739846726513489841296735953478261235941678469387512187625394
 3 9 4 | 8 6 2 | 1 5 7 
 6 7 8 | 1 5 4 | 9 2 3 
 5 1 2 | 7 3 9 | 8 4 6 
-------+-------+------
 7 2 6 | 5 1 3 | 4 8 9 
 8 4 1 | 2 9 6 | 7 3 5 
 9 5 3 | 4 7 8 | 2 6 1 
-------+-------+------
 2 3 5 | 9 4 1 | 6 7 8 
 4 6 9 | 3 8 7 | 5 1 2 
 1 8 7 | 6 2 5 | 3 9 4 


9 clues:

600000007040010080000000000000000000000805000000030000000000000000020000000000000
 6 . . | . . . | . . 7 
 . 4 . | . 1 . | . 8 . 
 . . . | . . . | . . . 
-------+-------+------
 . . . | . . . | . . . 
 . . . | 8 . 5 | . . . 
 . . . | . 3 . | . . . 
-------+-------+------
 . . . | . . . | . . . 
 . . . | . 2 . | . . . 
 . . . | . . . | . . . 

631958427742316589895274163589742316163895274427631958274163895958427631316589742
 6 3 1 | 9 5 8 | 4 2 7 
 7 4 2 | 3 1 6 | 5 8 9 
 8 9 5 | 2 7 4 | 1 6 3 
-------+-------+------
 5 8 9 | 7 4 2 | 3 1 6 
 1 6 3 | 8 9 5 | 2 7 4 
 4 2 7 | 6 3 1 | 9 5 8 
-------+-------+------
 2 7 4 | 1 6 3 | 8 9 5 
 9 5 8 | 4 2 7 | 6 3 1 
 3 1 6 | 5 8 9 | 7 4 2 

000000000000070000000605000000000000030000040002000100000802000000000000000000000
 . . . | . . . | . . . 
 . . . | . 7 . | . . . 
 . . . | 6 . 5 | . . . 
-------+-------+------
 . . . | . . . | . . . 
 . 3 . | . . . | . 4 . 
 . . 2 | . . . | 1 . . 
-------+-------+------
 . . . | 8 . 2 | . . . 
 . . . | . . . | . . . 
 . . . | . . . | . . . 

283149567456378912791625834914756328837291645562483179675832491129564783348917256
 2 8 3 | 1 4 9 | 5 6 7 
 4 5 6 | 3 7 8 | 9 1 2 
 7 9 1 | 6 2 5 | 8 3 4 
-------+-------+------
 9 1 4 | 7 5 6 | 3 2 8 
 8 3 7 | 2 9 1 | 6 4 5 
 5 6 2 | 4 8 3 | 1 7 9 
-------+-------+------
 6 7 5 | 8 3 2 | 4 9 1 
 1 2 9 | 5 6 4 | 7 8 3 
 3 4 8 | 9 1 7 | 2 5 6

tarek
User avatar
tarek
 
Posts: 2612
Joined: 05 January 2006

Postby udosuk » Sun Jul 13, 2008 3:17 am

tarek wrote:With a short run of the program, here are some DG ,DG diagonals, Diamonds, X puzzles with the lowest number of clues that displayed symmetry, the solution grids are also included in case somebody has some use for them:D .

Thanks! That was so cool.

I cracked your DDX002 but it required substancial chains and fishes to solve. Nothing elegant enough to post about.:(
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby tarek » Sun Jul 13, 2008 11:49 pm

udosuk wrote:I cracked your DDX002 but it required substancial chains and fishes to solve. Nothing elegant enough to post about.:(
I warned you:D Nevertheless, congrats

tarek
User avatar
tarek
 
Posts: 2612
Joined: 05 January 2006

Postby evert » Sun Oct 19, 2008 12:15 pm

tarek wrote:No Zorro moves then:(

Here is a double diamond X
Code: Select all
6 . 8|. 7 .|2 . 3
. . .|. . .|. . .
2 . .|. . .|. . 4
-----+-----+-----
. . .|7 . 5|. . .
1 . .|. . .|. . .
. . .|6 . 1|. . .
-----+-----+-----
7 . .|. . .|. . 5
. . .|. . .|. . .
4 . 3|. . .|6 . 2
mild advanced moves needed

tarek

I think I found 2 solutions:
Code: Select all
618479253
947532186
235816794
382745961
164398527
579621438
791263845
826154379
453987612

618479253
947532186
235816794
389725461
164398527
572641938
791263845
826154379
453987612
evert
 
Posts: 186
Joined: 26 August 2005

Postby Glyn » Sun Oct 19, 2008 2:55 pm

evertThe two solutions you have listed have 2X7's on the descending diagonal.
The one you should find is
Code: Select all
.------.------.------.
| 6 1 8| 4 7 9| 2 5 3|
| 3 4 7| 5 2 6| 9 8 1|
| 2 9 5| 8 1 3| 7 6 4|
:------+------+------:
| 9 3 4| 7 8 5| 1 2 6|
| 1 5 6| 2 9 4| 3 7 8|
| 8 7 2| 6 3 1| 5 4 9|
:------+------+------:
| 7 6 1| 3 4 2| 8 9 5|
| 5 2 9| 1 6 8| 4 3 7|
| 4 8 3| 9 5 7| 6 1 2|
'------'------'------'
Glyn
 
Posts: 357
Joined: 26 April 2007

Postby evert » Mon Oct 20, 2008 9:26 am

Indeed; I overlooked the X constraint was mentioned:idea:
evert
 
Posts: 186
Joined: 26 August 2005

Previous

Return to Sudoku variants