The New Sudoku Players' Forum

[udosuk]

Here is another 21-clue Sudoku:

Code: Select all

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

I have to apply 2 chains to solve this puzzle:

After basic techniques:

Code: Select all

 4      3      567    |*57     1      8      | 2     *67     9   
 16    *1579   15679  | 2     -569    3      | 8      1467   467
 2      179    8      | 479    69     479    | 5      167    3   
----------------------+----------------------+-------------------
 79     2      4579   | 1      8      469    | 479    3      56 
 8     *159    1459   | 3      7      469    | 149   *56     2   
 3      6      1479   | 49     2      5      | 1479   8      47 
----------------------+----------------------+-------------------
 79     4      3      | 579    59     1      | 6      2      8   
 16     179    1679   | 8      3      2      | 47     4579   457
 5      8      2      | 6      4      79     | 3      79     1   

[r2c5]=5=[r1c4]-7-[r1c8]-6-[r5c8]-5-[r5c2]=5=[r2c2]-5-[r2c5], so r2c5<>5

And then after some moves incl. colouring/xy-wing/turbot fish:

Code: Select all

 4     3     67    | 5     1     8     | 2    *67    9   
 16    157   156   | 2     9     3     | 8     46   -467
 2     9     8     | 47    6     47    | 5     1     3   
-------------------+-------------------+-----------------
*79    2     4579  | 1     8     46    | 479   3     56 
 8    *15    1459  | 3     7     469   | 149  *56    2   
 3     6    *147   | 49    2     5     | 1479  8    *47 
-------------------+-------------------+-----------------
*79    4     3     | 79    5     1     | 6     2     8   
 16   *17    169   | 8     3     2     | 47    459   457
 5     8     2     | 6     4     79    | 3     79    1   

[r2c9]=7=[r1c8]-6-[r5c8]-5-[r5c2]-1-[r8c2]=7=[r7c1]=9=[r4c1]-7-[r6c3]-4-[r6c9]-7-[r2c9], so r2c9<>7

Then the puzzle is solved...

Any more elegant path please!?

[JPF]

This is a real beauty worth do develop a more difficult pattern.

Thanks

Here is another 21-clue Sudoku:

Code: Select all

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

Claudia

to help udosuk , here is nearly the same, but very easy :

Code: Select all

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



JPF

[daj95376]

Any more elegant path please!?

[Edited:] My solver produces two chains. The first may be simpler than yours. The second is comparable and I won't list it.

(20*) Hidden Single, Naked Pair, (3*) Locked Candidate (1), Hidden Single, Naked Quad, and Locked Candidate (1) gets me to:

Code: Select all

*--------------------------------------------------------------------*

| 4      3      567    | 57      1     8      | 2      67     9      |
| 16     1579   15679  | 2      569    3      | 8      1467   467    |
| 2      179    8      | 479    69     479    | 5      167    3      |
|----------------------+----------------------+----------------------|
| 79     2      4579   | 1      8      469    | 479    3      56     |
| 8      159    1459   | 3      7      469    | 149    56     2      |
| 3      6      1479   | 49     2      5      | 1479   8      47     |
|----------------------+----------------------+----------------------|
| 79     4      3      | 579    59     1      | 6      2      8      |
| 16     179    1679   | 8      3      2      | 47     4579   457    |
| 5      8      2      | 6      4      79     | 3      79     1      |
*--------------------------------------------------------------------*


At this point, there's a short chain

Code: Select all

[r1c4]=7 => [r1c8]=6 => { [r1c3]=5, [r5c8]=5 } => [b4]=INVALID => [r1c4]=5


followed by a Hidden Single, (2*) Naked Pair, XY-Wing, and (4*) Naked Single. Then a second chain is needed before a cascade of Singles.

[Edited:] It's possible to find a single chain solution because there's a backdoor single at [r1c8]=7 that can be resolved using just Naked/Hidden Singles. Unfortunately, my notation skills aren't adequate to show the path for [r1c8]=6 => [c7]=INVALID. [Edited:] I don't recommend using this chain in a solution, but it makes a nice FYI.

[gsf]

FYI: There's a backdoor single at [r1c8]=7 for the grid above. Unfortunately, my notation skills aren't adequate to show the path of Naked/Hidden Singles for [r1c8]=6 => [c7]=INVALID.

there are 6 singles backdoors in bivalue cells

Code: Select all

[18]7[49]5[58]6[64]4[69]7[87]7

[daj95376]

[Edited: Discarded in favor of updating previous message.]

[claudiarabia]

Code: Select all

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

Claudia

[JPF]

Code: Select all

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

Claudia

Claudia,
There are two "9" in column 5.

JPF

[claudiarabia]

[code]. . 9 1 . 2 5 . .
Claudia,
There are two "9" in column 5.JPF

r5c5 must be 8. I have already corrected. Thanks a lot.

Claudia

[claudiarabia]

Claudiarabia wrote:

Code: Select all

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

This is a very good puzzle, and yes, it is harder than the previous one, but there is no need to dance. Carcul[/quote]
And here is the upgrade:

Code: Select all

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

Good look with solving!

Claudia

[claudiarabia]

If I would add r9c7 it would become to easy.

It is still quite easy:.....This pattern is also very pleasant: is it possible to make your puzzle harder, Claudiarabia?
Thanks, Carcul

Yes it is!

Code: Select all

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

Happy solving, Carcul!

Claudia

[ravel]

Code: Select all

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

Thanks for this one: 4 steps/Explainer rating 9.2.

[claudiarabia]

Code: Select all

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

Thanks for this one: 4 steps/Explainer rating 9.2.

My pleasure ! I made 3 versions of this pattern. Two of them Sudoku Explainer rated 9.0. I wonder if somebody ever reached the complete 10.

Claudia

[ravel]

I wonder if somebody ever reached the complete 10.

AFAIK not yet. Nicolas Juillerat, the author of Explainer, wrote me, that the hardest he constructed himself was 9.4 and the best he knew of 9.8 (toughest known).


Here is an esoteric collection - with more or less recognizable signs.

Code: Select all

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


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


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


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


All can be solved with basics (locked candidates, tuples), x(yz)-wing, UR (1,2,4) and turbot fish (note an easy to spot hidden quad in one puzzle).

Solving ones sign in a full moon night brings love, luck and money

For copying:

Code: Select all

..........31...98.8..6.7..55...4...76...3...2...1.2......8.1......5.4.....4...7..
.91...64.6..1.2..7...6.7......729.....4...8...1.....3..5.....1...2...3.....314...
.3517294...94.37.....9.8.....3...1....47.98....2...6.....6.7.....82.14...6759428.
...953....8...49..7...1..5.....8..3..67..58..8..4.....5..6...7..93...6....624....
....24......9..1.....1...3....3...5.....6..7..56.7..4.8..53..2.3..6....7.21......
..........345812...5.7.6.8..4.8.3.9..1.2.7.5..7.9.4.6..9.4.27.......8.......9....
............725.....6...8....1...2..275...3818.......6..........49.1.72.71.2.8.94
..4.6.....5.9.4....6.7.1....9.4.5....3.1.6..7.2.8.7.96.7.5.2..3.1.3..86..........
.....6173.......84......6.5....52..92...17....174......398......763.....8...7....
.6..41.27..23..5.......8.......39......6..8....94...5...31...4...582.9.....973...
..........31...76.46.9.52.33...64..5..........49...62.2.63.1.789..482..6.........
28.....39..6...1.....7.3......5.7....6931258....6.8......2.9.....1...3..34.....26


[claudiarabia]

AFAIK not yet. Nicolas Juillerat, the author of Explainer, wrote me, that the hardest he constructed himself was 9.4 and the best he knew of 9.8 (toughest known).

Hi ravel,

Thank you once for the esoteric collection!

Thank you twice for listing Fraulein in the world's toughest toughies!

In your toughies-list there are at least two puzzles which were rated by SE with 9,9.

with best wishes
Claudia

[claudiarabia]

Code: Select all

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

Claudia