The New Sudoku Players' Forum

[philvo]

Here are other variants of 6x6 puzzles :
X-sudokus with 5 givens and empty diagonals :

Code: Select all

  . . . 5 . .    . . . 5 . .    . . . . . .    . . . . . .    . . . . . .
  . . . 1 . .    . . . . . .    . . . . . .    . . 4 . . .    5 . . . . .
  . . . . 2 .    . . . . . .    . . . . 6 3    . . . . . 5    1 . . . . .
  . 4 . . . .    . . . . 3 2    . 1 . . 4 .    . . . . . 3    . . . . 2 3
  . . . 3 . .    6 . . . . .    . . . 2 . .    . . . . . .    . . 6 . . .
  . . . . . .    . . . 1 . .    . . . . . .    . . . 6 2 .    . . . . . .


X-sudokus with 5 givens and symmetry/diagonal :

Code: Select all

  . . . . . .    . . . . . .    . . . . . .    . . . . 3 .    2 . . . . .
  . 6 . . . .    . . . . 6 .    3 . . . . .    . . 5 . . .    . . . 5 . .
  . . . . . 2    3 . . . . .    . . . 2 . .    . 4 6 . . .    . . . . . 4
  . . . 4 . .    . . . . . .    1 . . . . .    . . . . . .    . 1 . . . .
  . . . . . .    1 . . . . .    . . . . . .    2 . . . . .    . . . . . .
  . . 1 . . 5    . 5 . 2 . .    . . 5 . 6 .    . . . . . .    . . 3 . . .


Hidden Text: Show

Code: Select all

...5.....1......2..4.......3........
...5..................326........1..
................63.1..4....2........
........4........5.....3.........62.
......5.....1.........23..6.........

.......6.........2...4..........1..5
..........6.3...........1......5.2..
......3........2..1.............5.6.
....3...5....46.........2...........
2........5.......4.1............3...


I hope you find them interesting.
phil

[jco]

Hi phil,

I hope you find them interesting.
phil

Very interesting! It was my first time solving an X-sudoku.
The additional powers that we gain from inferences along the diagonals are nice !
I have solved just the first one (in 5 main steps), but I need more practice
to be more efficient in finishing the puzzle.

Thank you for making available these puzzles.

[philvo]

Another set of 6x6 X-sudokus. Symmetric puzzles with 6 givens :

Code: Select all

  . . . . . .    . . . . . .    . . 4 5 . .    . 4 . . 1 .    . . . . . .
  . . . . . .    . . 2 4 . .    . . 3 4 . .    . . . . . .    . 6 . . 5 .
  3 . . . . 2    . . . . . .    . . . . . .    . 1 . . 3 .    1 . 5 2 . 4
  5 . . . . 6    . 6 . . 4 .    2 . . . . 6    . . . . . .    . . . . . .
  . . 4 5 . .    . . . . . .    . . . . . .    . 5 . . 2 .    . . . . . .
  . . . . . .    . . 1 5 . .    . . . . . .    . . . . . .    . . . . . .

  . . . . . .    3 4 . . . .    . . . . . .    2 6 5 . . .    . . . . . .
  . . . . . .    1 . . . . .    4 . 5 . 2 .    . . . . . .    . . . 4 6 1
  . . . . . .    . . . . . .    . . . . . .    . . . . . .    . . . . . .
  . 1 2 4 3 .    . . . . 6 .    . . . . . .    . . . . . 6    . . . . . .
  . . 1 5 . .    . . . 6 5 .    . 5 . 6 . 1    . . . . . 3    6 5 2 . . .
  . . . . . .    . . . . . .    . . . . . .    . . . . . 4    . . . . . .


Hidden Text: Show

Code: Select all

............3....25....6..45........
........24.........6..4.........15..
..45....34........2....6............
.4..1........1..3........5..2.......
.......6..5.1.52.4..................

...................1243...15........
34....1...............6....65.......
......4.5.2..............5.6.1......
265....................6.....3.....4
.........461............652.........


phil

[eleven]

This one is pretty hard

Code: Select all

. . . . . .
. . . . . .
. . . . . .
. 1 2 4 3 .
. . 1 5 . .
. . . . . .

+-------------------------+---------------------------+
| h1256   h23456   346    |   236     12456 gb3456    |
| h123456 i256     346    |   236     1456    12346   |
+-------------------------+---------------------------+
|  3456    3456    356    |  e16   eDc256   ed1256    |
| g56      1       2      |   4       3    fcb56      |
+-------------------------+---------------------------+
|  2346   a346     1      |   5     Da26     a2346    |
|  3456    2456    456    |   1236    1246    1236    |
+-------------------------+---------------------------+

I only found a complex net to eliminate 2r5c1 (later a kite 5 to finish)

Code: Select all

                             / -(5=62)r35c5
(2=634)r5c256 - (3|4=56)b4p26 - (6=512)r3c546 - 5r4c6 = r1c6&r4c1 - b1p124 = (5-2)r2c2 \
                                                                                         =2r1c1
                                     \ -2r6c6 .......................................... /
=> -2r5c1

[Edit: there are much easier moves to solve it, did not see the X-coloring tricks]

[jco]

I only found a complex net to eliminate 2r5c1 (later a kite 5 to finish)

Great move !! Hopefully, my understanding of it is close to your description.

Hidden Text: Show

For me, it was easier to see it as a double kraken.

Code: Select all

Kraken Diagonal (2)r1c1,r2c2,r5c5,r6c6 => -2* r5c1
(2)r1c1|r5c5*
||                           (5,6)r34c6&(1,2,6)r3c46.r5c5 - (5|6=342)r5c2.r1c5.r5c6*
||                          //
(2-5)r2c2 = b1p124 - r1c6&r4c1                                                  (6=3|4)r1c9,r5c2 - (3|4=62)r5c56*
||                          \\                                                  /
||                           (5)r4c6 - (5)r3c56|r1c9 = (126)r3c456 & (3|4|6)r1c9
||                                                                              \
||                                                                              (6=2)r5c8*
(2)r6c6 - (2=156)b4p136.r5c5 - (5|6=34)r1c1.r5c2 - (3|4=62)r5c56*


Thanks for sharing it. I must seek this way of reasoning for extreme Sudoku-X puzzles.