I have created a more approachable puzzle with this idea. I recommend trying that first before attempting this one. You can try it by clicking here.

Normal sudoku rules apply.

White dots between two cells indicate consecutive digits and black dots between two cells indicate a ratio of 1:2. For some rows and columns, the TOTAL number of white and/or black dots appearing in that row or column have been given. Dots on the border and outside the grid don't count.

You must place dots based on given clues (or the missing dots in case a few have already been given) entirely inside the grid to solve the puzzle.

A pair of orthogonal cells in the grid with 1 and 2 can have either a black or a white dot between them. It is left for the solver to deduce which one will it be. Also, there is no negative constraint in this puzzle, outside the grid or within the grid (i.e. all the possible kropki dots have NOT been given).

Here is an example on a 6*6 grid:

Good Luck. Have fun.

Penpa plus link

Normal sudoku rules apply.

White dots between two cells indicate consecutive digits and black dots between two cells indicate a ratio of 1:2. For some rows and columns, the TOTAL number of white and/or black dots appearing in that row or column have been given. Dots on the border and outside the grid don't count.

You must place dots based on given clues (or the missing dots in case a few have already been given) entirely inside the grid to solve the puzzle.

A pair of orthogonal cells in the grid with 1 and 2 can have either a black or a white dot between them. It is left for the solver to deduce which one will it be. Also, there is no negative constraint in this puzzle, outside the grid or within the grid (i.e. all the possible kropki dots have NOT been given).

Here is an example on a 6*6 grid:

Good Luck. Have fun.

Penpa plus link

Lösungscode: Column 1 Column 3

Zuletzt geändert Gestern, 19:18 Uhr

Gelöst von NikolaZ, smckinley

**Gestern, 09:33 Uhr von udukos**

Thank you so much, smckinley!

**Gestern, 05:30 Uhr von smckinley**

Fantastic! Quite the mental workout. Thank you @udukos!

**am 25. November 2020, 18:24 Uhr von Tilberg**

@udukos: Thank you!

Zuletzt geändert am 25. November 2020, 17:18 Uhr

**am 25. November 2020, 16:19 Uhr von Tilberg**

How do I place dots with Penpa?

@Tilberg You have to turn Border function ON.

Then in Mode, Select Shape.

Then Select Subheading Shape, select Circles from the dropdown menu, XS size.

You can now click on the borders between cells and type 1 to add a white dot and 2 to add a black dot.

Turn the Border off to go back to entering digits normally.

Also, I had personally recommend trying my second puzzle with the same ruleset before trying this one.

https://logic-masters.de/Raetselportal/Raetsel/zeigen.php?id=0004S1

**am 23. November 2020, 20:48 Uhr von udukos**

Updated rules description

Zuletzt geändert am 23. November 2020, 20:36 Uhr

**am 23. November 2020, 19:51 Uhr von Richard**

I am very fond of kropki (I mean the real kropki with the negative constraint; not only the ratio/consecutive dots.)

So I have looked to the puzzle and wondered how to disambiguate between black or white dots between 1 and 2. And why there is no dot between the given 2 and 3 outside the grid in row 6 of the example. And in column 2 of the example there are no consecutive digits in the 6x6-area. So there is a zero in the upper row outside the grid. But that is next to a 1 so there should be a dot.

With so much questions I decided to put it away again until it has solves.

@Richard Thank you for your feedback. There is no negative constraint in this puzzle, outside the grid or inside the grid. Only the given clues and kropki dots provide restrictions. A 12 pair can have either a black or a white dot between them. It is left to the solver to deduce what it will be. The example I have provided is a valid problem. One can solve it logically. It shows a white dot between 12 at one place and a black dot between 12 at two other places. If one were to solve that problem, they would understand how this was deduced. I will add this to the rules. And also the fact that there is no negative constraint. Though there is no negative constraint, I hope you still give it a try. :)

**am 23. November 2020, 15:37 Uhr von udukos**

I was expecting a few solves on this puzzle by now. Although entry into the puzzle is tough, it utilises interesting kropki logic. I would appreciate feedback from anyone who gives this a try. If you would like any hints, let me know in hidden comments.