The New Sudoku Players' Forum

[claudiarabia]

How many solutions ?

Code: Select all

 . . . . . . . . .
 . . 5 7 9 3 . . .
 . 2 6 . . . 9 . .
 . 8 . . . . 4 . .
 . . . . . 1 6 . .
 . . . . 5 6 . . .
 . . . 8 . . . . .
 . . 3 . . . . . .
 . 4 1 5 2 9 8 6 .



A great Idea. That's the only thing multiple solutions shall be allowed. But above 30 solutions it could become a problem.
Claudia
JPF

[daj95376]

After basic techniques, there are a number of assignments that result in a cascade of singles to finish the puzzle. Here's one.

Code: Select all

. . . . . . . . 9
. . . . . 3 . 6 .
. . 1 5 7 . 4 . .
4 . 8 . . . 2 . .
. 9 . . 8 . . 3 .
. . 5 . . . 7 . 1
. . 4 . 2 8 1 . .
. 1 . 6 . . . . .
3 . . . . . . . .

[r8c3]=7 => { [r8c6]=4, [r5c3]=2 } => [c4]=INVALID for <17> => [r8c3]=2


[ronk]

After basic techniques, there are a number of backdoor singles available to solve this puzzle. Here's one.

Code: Select all

. . . . . . . . 9
. . . . . 3 . 6 .
. . 1 5 7 . 4 . .
4 . 8 . . . 2 . .
. 9 . . 8 . . 3 .
. . 5 . . . 7 . 1
. . 4 . 2 8 1 . .
. 1 . 6 . . . . .
3 . . . . . . . .

[r8c3]=7 => { [r8c6]=4, [r5c3]=2 } => [c4]=INVALID for <17> => [r8c3]=2


The ALS xz-rule makes that same placement.

Code: Select all

 257  2457 3    |  248  46   246  | 58   1    9
 25   245  9    |  1248 14   3    | 58   6    7
 68   68   1    |  5    7    9    | 4    2    3
----------------+-----------------+---------------
 4    367  8    | B17   136  167  | 2    9    5
 1    9    27   | B27   8    5    | 6    3    4
 26   236  5    |  9    346  246  | 7    8    1
----------------+-----------------+---------------
 9    57   4    |  3    2    8    | 1    57   6
 2578 1   A27   |  6    9   A47   | 3    457  28
 3    28   6    | B147  5    147  | 9    47   28

 Sets: A = {r8c36} = {247}
       B = {r459c4} = {1247}
       x = 4, z = 2, implying r5c3<>2 and r8c3=2

At least one of r8c6<>4 and r9c4<>4 must be true. If r8c6<>4, the digits 27 are locked in set A. If r9c4<>4, the digits 127 are locked in set B. Therefore any 2s candidates that "see" all the 2s in both sets A and B may be excluded.

[Havard]

My favorite shape so far was posted here a while ago by Fermion: http://sudokuarchitect.com/forum/viewtopic.php?p=1916

He has done the other suits too!

Havard

[claudiarabia]

Code: Select all

. . . . . . . . .
. 8 6 . 2 . 9 7 .
. 2 . 9 . . 5 1 .
. 1 8 3 . . . 6 .
. . . . 4 . . . .
. 5 . . . 8 2 3 .
. 3 7 . . 4 . 5 .
. 9 2 . 6 . 4 8
. . . . . . . . .

I couldn't get a more difficult level without seeds in the edge. Did somebody?

Claudia

[RW]

I couldn't get a more difficult level without seeds in the edge. Did somebody?

I'm not quite sure what you mean with 'difficult level without seeds in the edge', but if you want harder puzzles with the pattern, here's a few:

Hard, but solvable for a human (and minimal):

Code: Select all

 *-----------*
 |...|...|...|
 |.83|.7.|91.|
 |.2.|9..|57.|
 |---+---+---|
 |.67|5..|.9.|
 |...|.4.|...|
 |.5.|..1|23.|
 |---+---+---|
 |.35|..2|.8.|
 |.72|.9.|36.|
 |...|...|...|
 *-----------*

Harder, but solvable for a carcul:

Code: Select all

 *-----------*
 |...|...|...|
 |.85|.7.|24.|
 |.2.|3..|51.|
 |---+---+---|
 |.17|2..|.9.|
 |...|.6.|...|
 |.5.|..8|47.|
 |---+---+---|
 |.38|..4|.2.|
 |.71|.9.|38.|
 |...|...|...|
 *-----------*

Drop the redundant clue and the easiest move in the starting grid is a naked/hidden quad:

Code: Select all

..........85...24..2.3..51..172...9.....6.....5...847..38..4.2..71.9.38..........

Finally I tried to chop a bit from the middle and the corners, preserving symmetry, but couldn't find any hard ones there:

Code: Select all

 *-----------*
 |...|...|...|
 |..9|.8.|2..|
 |.2.|4..|56.|
 |---+---+---|
 |.15|7..|.8.|
 |...|...|...|
 |.4.|..9|63.|
 |---+---+---|
 |.68|..4|.1.|
 |..1|.9.|7..|
 |...|...|...|
 *-----------*


RW

[JPF]

RW, I was just about to post this one :

Code: Select all

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



or this one :

Code: Select all

 . . . | . . . | . . .
 . 3 8 | . 2 . | 6 9 .
 . 2 . | 9 . . | 1 4 .
-------+-------+-------
 . 4 5 | 8 . . | . 2 .
 . . . | . 9 . | . . .
 . 9 . | . . 1 | 4 6 .
-------+-------+-------
 . 6 1 | . . 9 | . 3 .
 . 5 4 | . 3 . | 9 8 .
 . . . | . . . | . . .



and
an "included" pattern (easy 18 stepper) :

Code: Select all

 . . . . . . . . .
 . 7 8 . . . 1 2 .
 . 4 . 3 . . 5 6 .
 . 3 5 8 . . . . .
 . . . . . . . . .
 . . . . . 2 9 7 .
 . 2 4 . . 7 . 1 .
 . 8 6 . . . 2 3 .
 . . . . . . . . .



JPF

[claudiarabia]

Code: Select all

 *-----------*
 |...|...|...|
 |.85|...|24.|
 |.2.|3..|51.|
 |---+---+---|
 |.17|2..|.9.|
 |...|.6.|...|
 |.5.|..8|47.|
 |---+---+---|
 |.38|..4|.2.|
 |.71|.9.|38.|
 |...|...|...|
 *-----------*

Drop the redundant clue and the easiest move in the starting grid is a naked/hidden quad:
RW

Thank you for this one. Though without symmetry a great puzzle. Sudoku Explainer rates it with 8,3! And quads aren't that much to start with in other puzzles.

Claudia

[claudiarabia]

Code: Select all

. . . . . . . . .
. 2 4 . . . 8 6 .
. 8 . 7 . 5 4 . .
. 9 . . 4 8 . 1 .
. . . 2 . 3 . . .
. 4 . 1 7 . . 3 .
. . 2 3 . 6 . 8 .
. 3 9 . . . 7 2 .
. . . . . . . . .

For the lovers of turbot fisch and forcing X-chain. R5c6 can be omitted.

Claudia

[daj95376]

Claudia,

Did you catch the UR Type 1 on <58>? It eliminates the XY-Chain and make both variants of this puzzle have identical solutions.

[Update:] It occurs to me that you might be using an XY-Chain where Simple Sudoku chose to use Multi-Coloring. If so, then the UR Type 1 wouldn't affect your solution. I'm sorry if I only made things confusing!

[claudiarabia]

Claudia,

Did you catch the UR Type 1 on <58>? It eliminates the XY-Chain and make both variants of this puzzle have identical solutions.

No, I didn't. But I'll try. Thanks

Claudia

[claudiarabia]

Code: Select all

7 . 2 . 6 . 3 . .
. . . . . . . . 8
. 8 . 2 . 4 . . .
3 . . 1 . . . . 9
. . . . 5 . . . .
4 . . . . 2 . . 6
. . . 3 . 8 . 4 .
6 . . . . . . . .
. . 9 . 1 . 7 . 5

r9c7 may be omitted to get a higher difficulty-level.
Claudia

[ravel]

Oh, this one is (also) nice to solve, turbot fish, xyz-wing and a unique rectangle with x-wing. (But it seems to need chains without the 7.)
[Edit:] Apologies to those who wondered, how (with the 7) the puzzle can be solved without chains - i made a mistake.

[maria45]

I don't know if these true hearts are already known. Thanks to ajb:

Code: Select all

.15...26.
9..4.1..8
8...2...3
4.......6
2.......7
.6.....5.
..9...1..
...5.7...
....9....

.79...43.
6..2.5..9
3...7...5
8.......7
.2.....8.
.4.....6.
..6...5..
...7.4...
....1....


easy to solve, so just for the soft hearted.

[JPF]

A bit less easy :

Code: Select all

 . 2 4 . . . 6 7 .
 9 . . 7 . 5 . . 1
 3 . . . 2 . . . 8
 8 . . . . . . . 7
 6 . . . . . . . 2
 . 3 . . . . . 1 .
 . . 5 . . . 4 . .
 . . . 6 . 2 . . .
 . . . . 3 . . . .



JPF