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by **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

by **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.

by **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

by **tarek** » Sat Jun 21, 2008 10:48 am

Diamonds have always been desirable objects, just like beer

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|. . .

tarek

by **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

.

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

by **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 .

Thanks! That was so cool.

I cracked your DDX002 but it required substancial chains and fishes to solve. Nothing elegant enough to post about.

by **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

Nevertheless, congrats

tarek

by **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

by **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| '------'------'------'

by **evert** » Mon Oct 20, 2008 9:26 am

Indeed; I overlooked the X constraint was mentioned :idea:

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