## 13-clue Sudoku X

For fans of Killer Sudoku, Samurai Sudoku and other variants
Ruud wrote:Came across a 13-clue Sudoku-X which starts with 41 consecutive empty cells...

Wonderful! Half of the grid is totally empty! So what can you do next, 5 empty rows?

IMHO the reference about coordinate-system is totally BS (pardon for my bluntness). The original poster of that idea must be a non-mathematician, he/she can't even distinguish between discrete number system and real number system, let alone finity and infinity. Let's leave the coordinates to trigonometry and calculus and complex numbers and such...
udosuk

Posts: 2698
Joined: 17 July 2005

gsf wrote:each of these can be swapped independently (for 4 combinations including the identity)
Code: Select all
`r(46)c(46)`

After implementing this change in my canonicalization routine, invalid puzzles appeared in the results.

You need to swap rows 4-6 and columns 4-6 simultaneously, otherwise you are exchanging 2 pairs of digits between the diagonals. The number of pattern permutations is now 96. My program is now rechecking the earlier results.

Ruud
Ruud

Posts: 664
Joined: 28 October 2005

Ruud wrote:
gsf wrote:each of these can be swapped independently (for 4 combinations including the identity)
Code: Select all
`r(46)c(46)`

After implementing this change in my canonicalization routine, invalid puzzles appeared in the results.

You need to swap rows 4-6 and columns 4-6 simultaneously, otherwise you are exchanging 2 pairs of digits between the diagonals. The number of pattern permutations is now 96. My program is now rechecking the earlier results.

aha
invalid on the diagonals
good catch
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA

Ruud wrote:The number of pattern permutations is now 96.

According to my own research, the number of sudoku-X morphisms is twice the number of sudoku automorphisms of this "sudoku":
Code: Select all
`+-------+-------+-------+| 1 . . | . . . | . . 2 || . 1 . | . . . | . 2 . || . . 1 | . . . | 2 . . |+-------+-------+-------+| . . . | 1 . 2 | . . . || . . . | . . . | . . . || . . . | 2 . 1 | . . . |+-------+-------+-------+| . . 2 | . . . | 1 . . || . 2 . | . . . | . 1 . || 2 . . | . . . | . . 1 |+-------+-------+-------+`

There are 96 of them, so that makes it 192. It is twice because you can rotate 90 degress to swap diagonals, and those are too X-sudokus.
Mauricio

Posts: 1174
Joined: 22 March 2006

Ruud wrote:
Code: Select all
`. . .|. . .|. . .. . .|. . .|. . .. . .|. . .|. . .-----\-----/-----. . .|. . .|. . .. . .|. . 1|2 . .3 . .|. 4 .|. 5 .-----/-----\-----. . 2|6 . 7|. . .. . .|8 . .|. . 17 . .|. . .|3 4 .`

Ruud, I tried to solve this puzzle, and arrived at this state:
Code: Select all
` *-----------------------------------------------------------------------------* | 14      56789   3789    | 1245    678     2359    | 56      379     48      | | 2589    47      3789    | 45      678     359     | 56      1       239     | | 2589    56789   1347    | 145     678     359     | 48      379     239     | |-------------------------\-------------------------/-------------------------| | 589     145789  14789   | 37      2       6       | 48      39      3489    | | 89      4789    4789    | 37      5       1       | 2       6       3489    | | 3       2       6       | 9       4       8       | 1       5       7       | |-------------------------/-------------------------\-------------------------| | 14      14      2       | 6       3       7       | 9       8       5       | | 6       3       5       | 8       9       4       | 7       2       1       | | 7       89      89      | 25      1       25      | 3       4       6       | *-----------------------------------------------------------------------------*`

Then I couldn't find any elegant move to crack it. I could, using long contradiction chains, to prove r3c3=3 and r3c7=7 both lead to contradictions, and thus r3c3={14} and solve the puzzle. But it feels like trial and error to me.

Can you, or your program find any better way to solve it? Thanks!
udosuk

Posts: 2698
Joined: 17 July 2005

udosuk:

The key moves are:

Dual ALS-xz r1c13|r2c23|r3c3 vs. r9c3 x=8/9 => r45c3<>89
XY-chain r2c2-r4c4-r5c4-r5c3 => r3c3|r5c2<>4
3D colors (4)r2c4=(4)r2c2=(4=1)r1c1=(1)r3c3=(1)r3c4) => r3c4<>4

After this last move, the puzzle falls after a few coloring moves on digit 3.

Note: The dual ALS-xz allows you to perform the ALS twice, with the x & z digits swapped.

Hard, but no guessing required. I found worse...

Ruud
Ruud

Posts: 664
Joined: 28 October 2005

udosuk wrote:Wonderful! Half of the grid is totally empty! So what can you do next, 5 empty rows?

There's always the puzzle on the right.
Don't know who made it. Came across it once.

greetings

Para
Para

Posts: 46
Joined: 20 February 2007

Para wrote:Don't know who made it. Came across it once.

I happen to know who made it.

Apparently it's from a Japanese folk from the city of East Osaka. So there you go.

What I wanted to see is a Sudoku-X with 13 clues or fewer and 5 empty rows.

BTW:
Ruud wrote:After this last move, the puzzle falls after a few coloring moves on digit 3.

That's not true. After that you still need another colouring move on 7 to crack it. (Added later: it is actually a "pointing pair" move on the diagonal, which IMHO warrants at least a mentioning as normal non-X players wouldn't recognise it easily.)

I hated that "3D-colors". To me it smells and tastes like T&E. I think the Dual ALS-xz is very nice and the xy-chain is equivalent to a Y-Wing. I'll look for ways to work around that dreaded 3D-colors move.
Last edited by udosuk on Sat Aug 04, 2007 11:25 am, edited 1 time in total.
udosuk

Posts: 2698
Joined: 17 July 2005

Alright here is a brief walkthrough to resolve the puzzle from the state I last posted:
Code: Select all
` *-----------------------------------------------------------------------------* | 14      56789   3789    | 1245    678     2359    | 56      379     48      | | 2589    47      3789    | 45      678     359     | 56      1       239     | | 2589    56789   1347    | 145     678     359     | 48      379     239     | |-------------------------\-------------------------/-------------------------| | 589     145789  14789   | 37      2       6       | 48      39      3489    | | 89      4789    4789    | 37      5       1       | 2       6       3489    | | 3       2       6       | 9       4       8       | 1       5       7       | |-------------------------/-------------------------\-------------------------| | 14      14      2       | 6       3       7       | 9       8       5       | | 6       3       5       | 8       9       4       | 7       2       1       | | 7       89      89      | 25      1       25      | 3       4       6       | *-----------------------------------------------------------------------------*`

Dual ALS-xz: A=r1c1+r2c2+r123c3={134789}, B=r9c3={89}, x=8|9, z=9|8 => r45c3<>8|9
Y-Wing: r45c4={37}, r2c2,r5c3=4|7 => r3c3,r45c2<>4
d\: either r2c2=4 or r3c3=1 => r23c4 must have 5 => r19c4,r123c6<>5
r9c46=[25] => r1c6=2 (hidden single c6) => r1c14={14} => r1c9=8
Turbot fish: strong links of 3 in r1c38, r3c3+r4c4 => r4c8<>3 => r4c8=9
Box-line interaction: 9 on r1 locked in b1 => r23c123<>9
r5c1=9 (hidden single c1) => r5c2=8 (hidden single r5) => r9c2=9
r1c3=9 (hidden single r1,c3,b1) => r1c8=3 (hidden single r1) => r3c8=7
Pointing pair: 7 on d\ locked in r2c2+r4c4 => r4c2<>7
r4c12=[51] => r27c2=[74] => r4c4=3 => all naked singles

No chains, no colouring move. However, the 3rd line is a bit of elaborated logic, and one can argue it steps on the boundary of T&E.

I've actually proposed it as a new form of ALS in this thread.
udosuk

Posts: 2698
Joined: 17 July 2005

This web page claimes to have (currently) 5503 12-clue Sudoku-X puzzels, like
Code: Select all
`\---+---+---/|...|...|...||...|...|...||...|...|...|+---\---/---+|...|...|12.||...|3..|.4.||..5|.67|...|+---/---\---+|..8|...|..6||.1.|4..|...||...|...|..8|/---+---+---\`
kjellfp

Posts: 140
Joined: 04 October 2005

kjellfp wrote:This web page claimes to have (currently) 5503 12-clue Sudoku-X puzzels

Of course, it is Ruud'd website.
Mauricio

Posts: 1174
Joined: 22 March 2006

Sorry, I got the impression that 12s where unknown, and apparently didn't read the thread good enough.
kjellfp

Posts: 140
Joined: 04 October 2005

The collection has now grown to 7193, but no 11 yet. Growth is slowing down a bit.

I haven't found a Sudoku-X with 5 empty rows and minimum number of clues, but this one is pretty close:

Code: Select all
`. . .|. . .|. . .. . .|. . .|. . .. . .|. . .|. . .-----\-----/-----. . .|. . .|. . .. . .|. . .|. . 1. . 2|3 4 5|. . .-----/-----\-----5 6 .|. . .|. . .1 . .|. . .|. 7 .. . .|8 . .|2 3 .`

Ruud
Ruud

Posts: 664
Joined: 28 October 2005

The latest one is not nearly as evil as the first two, but still need a reasonably tricky step to resolve:
Code: Select all
` *--------------------------------------------------------------------* | 38     79     1      | 49     2      6      | 3479   489    5      | | 269    38     679    | 5      78     349    | 3479   1      23479  | | 29     5      4      | 1     @78     39     | 6     @89    -2379   | |----------------------\----------------------/----------------------| | 3689   348    69     | 2      1      7      | 3489   5      349    | | 37     34     5      | 6      9      8      | 347    2      1      | | 789    1      2      | 3      4      5      | 789    6     #79     | |----------------------/----------------------\----------------------| | 5      6      8      | 7      3      2      | 1     *49    #49     | | 1      2      3      | 49     6      49     | 5      7      8      | | 4      79     79     | 8      5      1      | 2      3      6      | *--------------------------------------------------------------------*`

ALS-xy-wing:
ALS A (@): r3c58={789}
ALS B (#): r67c9={479}
ALS C (*): r7c8={49}
restricted common between B,C: x=4
restricted common between A,C: y=9
common between A,B: z=7

Therefore r3c9<>7, and singles solve the rest.

Unfortunately I can't find a simple ALS-xz to resolve this.

I'd like to call this move a "semi-Y-Wing" because if r3c8 was {79} instead of {89} it would be just a normal Y-Wing.

And now r3c58 combined is effectively performing the role as a single cell of {79} in r3c8.

People who are into chains will also find it as a very simple xy-chain (I'm not one of them).

Ruud, is there any 12-clue Sudoku-X which is solvable using singles only? There're plenty of singles-solvable 17-clue Sudoku puzzles.

PS:
My latest moderator priviledges allowed me to change Para's image to a a pic link (I hope he doesn't mind), thus restoring the normal width of this very page for my tiny 1024x768 laptop screen. Way cool!

It's funny when I edit others' posts the "Last edited by..." messages don't appear, but when I edit my own they do. I guess it's fair that I can't change the things I wrote in the past without others noticing.
udosuk

Posts: 2698
Joined: 17 July 2005

Previous