The New Sudoku Players' Forum

[denis_berthier]

The grid structure is the same as in Kakuro (cells with 0 correspond to black cells), but the game avoids all the tedious sum checking work required by Kakuro.

One difference is that in Zerodoku not all zeroes are necessarily given as clue. They must be located during the solving process.

OK. I hadn't tried to solve your examples and I had overlooked this point. It makes it all quite different, but still interesting. I guess generating minimal puzzles is hard.
With this definition, my other remarks are pointless.

I had considered developing an interface to my general CSP-Rules solver for this game (it would have been an easy adaptation of the interface I have developed for Kakuro), but the non-given "black cells" require more adaptation work than I have time to do now. However, it does not look too difficult and I'll keep this in mind.

What do you think of the game as I had first understood it ? - let's call it Cross-Lists (if it does not already exist !!!).

[evert]

What do you think of the game as I had first understood it ? - let's call it Cross-Lists (if it does not already exist !!!).

That's the series- or list-idea applied to Kakuro. Would be interesting too. Maybe also in Killer (Serial Killer ).

Mainpoint in Zerodoku was to have the solver locate the groups where the remaining constraints apply.

[evert]

Code: Select all

...|...|...
...|...|...
...|...|...
---+---+---
28*|***|*..
...|...|...
...|...|...
---+---+---
...|...|...
...|...|...
...|...|...


A segment containing 2 and 8 requires at least 7 positions where thus no zero is possible.

I've implemented this technique in the solver. Now the puzzles are a little bit more difficult, but without the trial-and-error factor.

8x8:

Code: Select all

3|4|.|7|.|.|.|3
4|5|.|8|7|.|6|5
0|.|.|0|.|7|.|.
.|.|4|.|0|.|.|6
7|4|1|.|2|.|.|.
.|5|.|9|3|.|8|.
.|.|3|.|.|0|.|6
9|.|.|.|.|0|8|0


9x9 ( ):

Code: Select all

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


10x10:

Code: Select all

.|2|.|.|.|8|.|.|.|.
2|.|.|.|8|7|.|2|4|.
.|4|.|.|0|6|.|5|.|.
.|.|1|.|3|.|0|.|.|4
4|.|.|0|.|.|.|.|0|1
1|.|0|.|1|0|.|.|.|8
0|.|.|.|.|.|5|.|5|.
.|7|.|5|0|3|.|0|6|.
.|.|9|1|.|.|.|.|.|.
.|4|.|.|.|4|0|5|.|.


[Serg]

Hi, evert!

Code: Select all

 ; ; ; ;0;3; ;3
 ; ;9;0;0;5; ;
8;2; ; ; ;4; ;
 ; ; ;5; ; ; ;
9;7; ; ; ;6;7;
7;6; ; ; ;7;9;6
 ; ;0; ; ; ; ;0
8; ;3; ;8;4; ;


Also tough...

I solved this puzzle. It is really tough. First I came to position:

Code: Select all

6 . . . 0 3 0 3
7 8 9 0 0 5 . .
8 2 . 6 . 4 3 .
0 . 6 5 . 0 . .
9 7 8 0 . 6 7 .
7 6 0 8 5 7 9 6
6 5 0 7 6 5 . 0
8 0 3 6 8 4 5 7


Then I used T&E method (locally, w/o pencilmarks) - I checked can cell r3c8 contain zero? It turns out r3c8 must contain zero, so we can easily get solution:

Code: Select all

6 4 7 5 0 3 0 3
7 8 9 0 0 5 6 4
8 2 5 6 7 4 3 0
0 3 6 5 4 0 8 7
9 7 8 0 9 6 7 8
7 6 0 8 5 7 9 6
6 5 0 7 6 5 4 0
8 0 3 6 8 4 5 7


It took me 2 hours to solve this puzzle. I feel 8x8 size is too small - as you can see digits "1" are totally absent, digit "2" appears once only. I think optimal zerodoku size lies in the range 9x9 - 12x12.

Thank you for interesting puzzle!

Serg

[Serg]

Hi, evert!
I solved (on vacations) your puzzle

Code: Select all

3;5; ; ;7; ; ;3; ;3; ;
0; ; ; ; ; ; ; ; ; ;2;1
 ; ; ; ;7; ; ;9; ; ; ;
4;0; ;7;9;6; ;4; ; ;6;
9; ; ; ; ; ; ; ; ;0; ;
 ;7;0; ;6;8; ;7;9; ; ;8
 ; ;0;2; ;9;4; ;3; ;7;
 ;9; ;0; ;3;2; ; ; ; ;8
5; ;3; ;1;6; ; ; ; ; ;
 ; ; ; ; ;4; ;0;0;6; ;
 ;4; ; ; ; ;0; ; ;8; ;6
5; ; ; ;4; ; ;3;8; ;0;9


posted on October, 5.
Nice puzzle! It is not "tough" in the sense that it can be solved by basic solution methods only, without T&E. But it is very complicated. It took me 6 hours of pure time to solve it. Congratulations! To my mind it is the best zerodoku puzzle I solved (yet).

Serg

[evert]

I think optimal zerodoku size lies in the range 9x9 - 12x12.

Since I also implemented the extra technique for excluding zeroes, it could be nice to generate some more 10x10 and larger:

Code: Select all

6| | | | | | |2|1|
 | |1|4| |2| |1| |
 |8|0| |0|4| |6| |2
 |9| | |0| | | | |0
 |7|6| | | | | | |6
9| | |8| |6| | | |0
 | |8|9|5|0|1| |5|4
 | | | |7| |6| | |3
7| |6| | | |4|5|3|
5|0| | | |2|0| |2|


 | |9| | | |0|3| |5
 |7| | | | | | |0|0
0| | |9| |7| | | |
7| |7|6| |5| | |3|6
 | |5| |2| | | | |7
6| | | |5|9|0|4| |0
 |7|0| | | |3|6| |
0| | |2| |6|5|8| |
 | |9|0| | | | | |
6| |8|3|2|7| |5|6|


5|7| |8| |5| |0|2| |
2| |0|6| | |3|5|1| |
 |7| |9| |0| | | |5|
 | | | | |7| | | | |4
 |3| | | | |6| | | |
 | | |0| | |9| | | |
7|6| | | | | |3|8| |6
8| | |2| |7| | | | |4
 | | | |3|5| |7|0| |0
6| | |5|4|9|7|2| | |
 | |1| |8|4|2|6| |8|7


5| | | | |1|4|9|5| |
1| |7|8|9| |2| |6| |3
 |4| | | |5|9|3| |7|0
 | | |7| | | |8| | |
 | | |5| | | |7|9| |
 | |4| |7| | |5| | |
 |7| |5|8|1| | | | |
0| | | | | | | | | |
 | |7|8|9| | | | | |0
3|1| | | |2| |5|0|0|9
0|6|2| | | | | |9|6|


 |5| | |2|1|7| |0|6|8|
7|8| |0|6| |8| | | | |0
 | |6|9| | | |5|1| |7|0
 | |5| | |3| | | | | |
 | | |0| |2|3| |6| |4|1
 |9| |5| | | |0| |9| |
 |2| | |9| | |1| |6|0|
 | | |3| | | |5| | | |
2| | | | |5|1|2| | |2|
3|5| | | | | |3|8| | |
 |6|2| |5|3| | |7|8| |
 | | | |6|1|2|4| |3| |2


4| |4| | |3| | | | | |0
 | | |5|1| | |5| | |9|7
 |5| | | | | |7|9| |5|
 | | | |0| |4| | |3|4|
5|3|7|4| | | |8| | | |
 | |3|5| | |5| | |3| |
 |9| | |7| | | | | | |
 |8| | | |5| | |5|4| |
4|6| | |5| |0| | |5|4|
 | |7| | | |2|5|0| | |2
 |7| |8| | |3| |3| | |
4|5| |2|4| |0|7| |3|5|


Solutions:

Hidden Text: Show

Code: Select all

6|5|2|3|4|0|3|2|1|4
5|6|1|4|3|2|0|1|2|3
7|8|0|7|0|4|5|6|3|2
8|9|7|6|0|3|2|5|4|0
0|7|6|2|8|5|3|4|0|6
9|0|5|8|9|6|7|3|4|0
6|7|8|9|5|0|1|0|5|4
8|9|0|5|7|3|6|4|0|3
7|8|6|0|6|1|4|5|3|2
5|0|5|3|4|2|0|3|2|1


4|8|9|5|7|6|0|3|4|5
5|7|6|3|9|8|2|4|0|0
0|6|4|9|8|7|5|0|4|5
7|0|7|6|0|5|4|2|3|6
9|6|5|8|2|4|3|7|0|7
6|4|8|7|5|9|0|4|3|0
8|7|0|4|3|0|3|6|5|4
0|5|0|2|4|6|5|8|7|3
7|8|9|0|0|5|6|3|4|2
6|0|8|3|2|7|4|5|6|1


5|7|6|8|0|5|4|0|2|3|1
2|0|0|6|7|4|3|5|1|8|2
6|7|5|9|8|0|0|6|4|5|3
3|2|4|5|0|7|8|0|5|6|4
4|3|6|7|5|0|6|5|7|4|0
0|4|3|0|6|8|9|4|3|7|5
7|6|0|4|7|6|5|3|8|0|6
8|5|4|2|9|7|3|1|6|0|4
9|8|2|6|3|5|4|7|0|7|0
6|0|3|5|4|9|7|2|1|6|8
5|7|1|3|8|4|2|6|0|8|7


5|0|8|6|7|1|4|9|5|3|2
1|0|7|8|9|0|2|4|6|5|3
3|4|0|4|6|5|9|3|8|7|0
6|9|5|7|8|0|7|8|4|6|5
7|8|6|5|0|5|8|7|9|4|6
2|3|4|0|7|4|6|5|1|2|3
4|7|9|5|8|1|3|6|2|0|4
0|2|3|6|4|7|5|0|3|4|2
4|5|7|8|9|6|0|6|7|5|0
3|1|8|7|6|2|4|5|0|0|9
0|6|2|4|5|3|0|7|9|6|8


4|5|3|8|2|1|7|6|0|6|8|7
7|8|9|0|6|5|8|4|2|7|3|0
8|7|6|9|3|4|2|5|1|0|7|0
9|4|5|8|7|3|6|0|5|0|5|4
5|6|4|0|5|2|3|8|6|7|4|1
6|9|7|5|8|0|4|0|7|9|6|8
0|2|8|7|9|4|5|1|3|6|0|5
4|3|0|3|1|2|0|5|4|2|3|6
2|0|3|6|4|5|1|2|0|4|2|3
3|5|4|2|0|6|2|3|8|5|4|7
1|6|2|4|5|3|0|6|7|8|5|9
0|7|5|8|6|1|2|4|9|3|0|2


4|0|4|6|2|3|1|9|7|5|8|0
3|4|2|5|1|0|6|5|8|4|9|7
0|5|6|0|3|4|8|7|9|2|5|6
9|6|8|7|0|5|4|3|0|3|4|5
5|3|7|4|9|6|2|8|1|0|6|0
6|0|3|5|4|0|5|6|4|3|7|8
8|9|5|1|7|6|3|4|2|0|0|5
7|8|0|6|8|5|7|0|5|4|2|3
4|6|8|9|5|7|0|6|3|5|4|7
0|4|7|3|6|8|2|5|0|1|3|2
5|7|6|8|0|4|3|0|3|2|1|4
4|5|0|2|4|3|0|7|4|3|5|6


[Serg]

Hi, evert!
Last week I had possibility to solve your puzzles posted by you on November, 27. I enjoy your zerodoku puzzles, but unfortunately I have spare time to solve them on vacations only (going by train). I managed to solve both 10x10 puzzles and both 11x11 puzzles. Thank you for interesting game! I think you can be interested in my rating of these puzzles, so I post my opinion below.

Code: Select all

10x10 zerodoku number 1

6| | | | | | |2|1|
 | |1|4| |2| |1| |
 |8|0| |0|4| |6| |2
 |9| | |0| | | | |0
 |7|6| | | | | | |6
9| | |8| |6| | | |0
 | |8|9|5|0|1| |5|4
 | | | |7| |6| | |3
7| |6| | | |4|5|3|
5|0| | | |2|0| |2|

I think, this is moderate difficulty puzzle. I spent 2.5 hours to solve it.

Code: Select all

10x10 zerodoku number 2

 | |9| | | |0|3| |5
 |7| | | | | | |0|0
0| | |9| |7| | | |
7| |7|6| |5| | |3|6
 | |5| |2| | | | |7
6| | | |5|9|0|4| |0
 |7|0| | | |3|6| |
0| | |2| |6|5|8| |
 | |9|0| | | | | |
6| |8|3|2|7| |5|6|

I think, this is difficult puzzle, but not tough, because it can be solved by basic techniques only. I spent 3 hours to solve it. This puzzle is one of my favorite zerodoku puzzles.

Code: Select all

11x11 zerodoku number 1

5|7| |8| |5| |0|2| |
2| |0|6| | |3|5|1| |
 |7| |9| |0| | | |5|
 | | | | |7| | | | |4
 |3| | | | |6| | | |
 | | |0| | |9| | | |
7|6| | | | | |3|8| |6
8| | |2| |7| | | | |4
 | | | |3|5| |7|0| |0
6| | |5|4|9|7|2| | |
 | |1| |8|4|2|6| |8|7

I think, this is moderate difficulty puzzle. I spent 2-2.5 hours to solve it.

Code: Select all

11x11 zerodoku number 2

5| | | | |1|4|9|5| |
1| |7|8|9| |2| |6| |3
 |4| | | |5|9|3| |7|0
 | | |7| | | |8| | |
 | | |5| | | |7|9| |
 | |4| |7| | |5| | |
 |7| |5|8|1| | | | |
0| | | | | | | | | |
 | |7|8|9| | | | | |0
3|1| | | |2| |5|0|0|9
0|6|2| | | | | |9|6|

This is very difficult puzzle for me, but not tough, because it can be solved by basic techniques only. I spent a day to solve it. (I was forced 3 times to start from scratch because of my errors in solving process.) I think this puzzle is champion zerodoku puzzle. Well composed puzzle!

Can you compose zerodoku puzzle without zeroes in initial configuration? It could be curious if a 9x9 zerodoku puzzle could exist that can be treated as sudoku puzzle and zerodoku puzzle at the same time.

One observation. Zerodoku has its own unavoidable sets, the smallest possible UA contains 2 cells only.

Thank you for your work!

Serg

[evert]

My zerodoku solver & generator is available online.