The New Sudoku Players' Forum

[claudiarabia]

What i remember in this context is, that in the last elections in my country some ballots were blighted with this sign, but 95% of them were the other way round (the sun symbol).

Thank you very much

Claudia

[m_b_metcalf]

I was looking through my archive, and found these two 'squarish' puzzles. I was surprised that the second one is that hard, given that the central box is full.

Code: Select all

  3  .  5  4  .  2  7  .  1
  9  .  .  1  .  6  .  .  8
  .  .  .  .  .  .  .  .  .
  .  .  8  2  .  5  1  .  .
  .  .  .  .  .  .  .  .  .
  .  .  7  8  .  1  2  .  .
  .  .  .  .  .  .  .  .  .
  1  .  3  .  .  .  6  .  4
  .  .  4  9  .  7  5  .  .  SE 7.2


Code: Select all

   .  . 8  9  .  1  6  .  .
  2  .  .  .  .  .  .  .  5
  .  7  .  .  .  .  .  9  .
  .  8  .  4  5  2  .  6  .
  3  .  .  7  .  8  .  .  1
  .  5  .  1  9  3  .  8  .
  .  3  .  .  .  .  .  7  .
  4  .  .  .  .  .  .  .  9
  .  .  5  3  .  4  2  .  .  SE 7.3


Regards,

Mike Metcalf

[m_b_metcalf]

Speaking of full boxes, there are over 280,000 grids that have the ordered 1-9 pattern in each of the three diagonal boxes. Below is an example of a mimimal puzzle derived from such a grid, where minimal here implies that those diagonal boxes are protected. I find the minimum number of additional clues to be 6. Are there smaller solutions?

Code: Select all

  1  2  3  .  .  .  .  9  .
  4  5  6  .  .  .  .  .  7
  7  8  9  3  .  .  .  .  .
  .  .  .  1  2  3  .  .  .
  .  .  7  4  5  6  .  .  .
  .  .  .  7  8  9  .  .  .
  .  .  .  8  .  .  1  2  3
  .  .  .  .  .  .  4  5  6
  .  .  5  .  .  .  7  8  9     six extra clues, SE 7.3


Regards,

Mike Metcalf

[Mauricio]

A beautiful sudoku; ER 8.3, minimal, fully symmetrical and nice clues given,
note the diagonal groups of 1's, 3's, 5's, 7's

Code: Select all

9...6...3
.8.7.5.9.
..7.9.5..
.7.....5.
8.6...2.4
.1.....3.
..1.4.3..
.6.1.3.2.
7...2...1

In the same league, though not minimal

Code: Select all

5...6...7
.2.7.5.4.
..7.4.5..
.7.....5.
8.6...2.4
.1.....3.
..1.8.3..
.9.1.3.6.
3...2...9

[m_b_metcalf]

I find the minimum number of additional clues to be 6. Are there smaller solutions?

To answer my own question, here's one with just 5 extra clues:

Code: Select all

  1  4  7  .  .  .  .  .  .
  2  5  8  .  3  .  4  .  .
  3  6  9  .  .  .  .  .  .
  .  .  .  1  4  7  .  .  .
  .  .  .  2  5  8  .  .  6
  .  .  .  3  6  9  .  .  .
  .  .  .  .  .  .  1  4  7
  .  .  6  .  .  .  2  5  8
  .  8  .  .  .  .  3  6  9   SE 8.4


Regards,

Mike Metcalf

[JPF]

Interesting question !
There are 283576 solutions to this puzzle :

Code: Select all

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



I find the minimum number of additional clues to be 6. Are there smaller solutions?

To answer my own question, here's one with just 5 extra clues:

Code: Select all

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



Nice !

It looks like a question we had here.

JPF

[m_b_metcalf]

Nice !

It looks like a question we had here.

JPF

Yes, except that the clues in the full boxes are identically ordered. Here's another, still with 5:

Code: Select all

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


Regards,

Mike Metcalf

[claudiarabia]

May I introduce Frauke to you?

Code: Select all

1..3..9..
.5...7.1.
..6.....2
8..4...3.
....3....
.7...6..5
4.....7..
.9.1...4.
..8..5..6


Frauke

S.E. has the rather rare 7.9 It shows also 3 Swordfisches and one Jelly

Code: Select all


1..3..8..
.2...7.1.
..6.....4
8..4...2.
....5....
.7...6..5
3.....7..
.9.1...4.
..4..5..6

S.E. 8.4 r8c8 or r9c3 omittable

Claudia

[daj95376]

May I introduce Frauke to you?

Code: Select all

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


Hidden Single, 3x Naked Quad, 2x Swordfish, and a Kraken X-Wing for starters. Nice introduction!!!

[Mauricio]

Chect out this sudoku, it has diagonal symmetry, but not only that, in this sudoku almost all clues given have diagonal symmetry too (ie, if a clue is given with number m, then its diagonal partner has number m too), only r1c3 and r7c9 don't follow that rule.
It is minimal and has ER 9.3.

Code: Select all

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


We can add 2's to get an aesthetically better sudoku, though not minimal

Code: Select all

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

Or we can add a 3, so now there are 25 (edit: first I counted 17, I forgot to count the symmetric ones, ) (9 of them in the diagonal) clues such that its diagonal partner has the same number given.

Code: Select all

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

In a sudoku (minimal or not minimal), what is the maximum number of clues given such that the diagonal partner of each clue given has the same number?

[claudiarabia]

Code: Select all

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


Code: Select all

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


And an SE 9.0-version

[claudiarabia]

Here’s an other 19 clues, with diagonal symmetry.

Code: Select all

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


SE=7.2 JPF

I couldn't resist to solve this beautiful bee. Maybe my forcing chains are longer than needed, but nevertheless it took me 4 steps only after the Pointing/Claiming/Single-Stuff to get to the solution.

Code: Select all

 *-----------*
 |1..|.62|..3|
 |.42|357|...|
 |.36|...|72.|
 |---+---+---|
 |.2.|6..|.37|
 |35.|78.|692|
 |76.|.23|...|
 |---+---+---|
 |..3|.7.|2..|
 |...|29.|34.|
 |2..|.36|.79|
 *-----------*

 
 *--------------------------------------------------------------------*
 | 1      789    5789   | 489    6      2      | 4589   58     3      |
 | 89     4      2      | 3      5      7      | 189    168    168    |
 | 589    3      6      | 1489   14     1489   | 7      2      458    |
 |----------------------+----------------------+----------------------|
 | 489    2      1489   | 6      14     59     | 1458   3      7      |
 | 3      5      14     | 7      8      14     | 6      9      2      |
 | 7      6      1489   | 59     2      3      | 1458   158    1458   |
 |----------------------+----------------------+----------------------|
 | 45689  189    3      | 1458   7      1458   | 2      1568   1568   |
 | 568    178    578    | 2      9      158    | 3      4      1568   |
 | 2      18     458    | 1458   3      6      | 158    7      9      |
 *--------------------------------------------------------------------*


I found four chains to solve this puzzle: The first and the third have subchains:

1. Elimination of 5 in r1c3=5 --> r1c2=7 --> r1c8= 8 --> r1c47=49 and r2c1=8 --> r2c7=9 and r3c1=9 --> r4c1 =4 --> r4c5=1 --> r3c5=4 --> r1c4=9 --> r1c7=4 --> r3c9=5 | if r1c4=9 --> r6c4 =5 --> r6c8=1 --> r2c8=6 --> r7c8=5 --> r7c1=6 --> r8c1=5 --> r9c4=5 ≠ r6c4=5 --> r3c1=5

2. Elimination of 5 in r1c7=5 --> r1c8=8 --> r1c23=79 --> r2c1=8 and r1c4=4 --> r3c5=1 --> r4c5=4 --> r5c6=1 --> r5c3=4--> r7c1=4-->r9c4=4 ≠ r1c4=4 --> r1c8=5

3. Elimination of 9 from r1c2: --> r2c1=8 --> r8c1=6 --> r79c2=18 and r7c1=9 --> r4c1=4 --> r4c5=1 --> r3c5=4 --> r1c4=8 --> r1c3=7 and r1c7=4 --> r2c7=9 and r3c9=8 --> r2c89=16
| if r8c1=6--> r8c2=7 --> r8c3=5 --> r8c9=1--> r2c9=6 --> r2c8=1 --> r6c8=8--> r7c8=6 --> r7c9=5 --> r9c7=8 --> r9c2=1 --> r9c4=5 --> r6c4=9 --> r4c6=5 --> r4c7= empty. (1in r4c5, 8in r6c8, 4in r4c1) -->r7c2=9

4. Elimination of 4 from r4c1 --> r4c5=1 --> r3c5=4 --> r1c7=4 --> r8c7=9 --> r2c1=8 --> r78c1=6 (one number missing) --> r7c1=4

Then the puzzle is practically solved.

Claudia

[claudiarabia]

We can add 2's to get an aesthetically better sudoku, though not minimal

Code: Select all

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

the spinning top motive is always good for setting milestones in sudoku-creating. Let me present a minimal one with some lesser clues and lesser difficulty.

Code: Select all

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


Minimal, ER 7.1. When you cange r8c2 to 5 you will get an ultra-easy sudoku out of this.

Code: Select all

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


Something more difficult (ER 8.5)

claudia

[JPF]

Code: Select all

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

In a sudoku (minimal or not minimal), what is the maximum number of clues given such that the diagonal partner of each clue given has the same number?

Here is a puzzle with 35 clues.
33 clues have their diagonal partner with the same digit.

Code: Select all

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



and better :
Here is a puzzle with 39 clues.
37 clues have their diagonal partner with the same digit :

Code: Select all

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



JPF

[Mauricio]

Here is a puzzle with 39 clues.
37 clues have their diagonal partner with the same digit :

Code: Select all

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



JPF

Very impressive, JPF.

Here is one with 42 clues, 39 of them "partnered".

Code: Select all

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