Logic Masters Deutschland e.V.

I had a lot of fun setting a Kropki Pairs puzzle recently so I set one more. This time additionally with the Anti-King constraint which is an old infamous friend of mine (I published an Anti-♔ series a year ago).

Though one or two deductions are possibly a little harder, I think that this puzzle is still on a 2/5 difficulty. Either way, I hope you enjoy the interactions between the two constraints!

Play online: f-puzzles | CtC app

Standard Sudoku rules apply
❶ Anti-King: cells that are a king's move apart in chess cannot contain the same digit
❷ Kropki: Cells separated by a white dot are consecutive, cells separated by a black dot have a 1:2 ratio.
No negative constraint, so not all possible dots are given.

1. The black dots around row 3 and 4 are heavily affected by the anti king constraint and can all be resolved to some pairs. Two of the four white dots connected with those cells are also affected by the anti king constraint.
2. After doing some Sudoku and the upper white dot the following question should help:
3. where does the 1 go in box 2?
4. The triple in r789c5 helps to reduce the options in box 7:
5. Because of the 2 the black dot in r78c3 can be only a 3/6 and
6. Because of the 4/5 the white dots in r8c123 can either be 8/7/6 or 1/2/3.
7. There are some further restrictions in box 7, the following question is key: where do 4/5 go in box 7? Answer: 4/5 in box 7 can only go in r7c12 (otherwise either 4 or 5 could not be entered)
8. Now, due to the anti king constraint, r67c67 forms a 6/7/8/9 quadrupel.
9. The pointing pair of 8s in box 5 leads only one place for the 6 which resolves the four digits
10. Now there is a 3/6 pair in r8 which does two things:
11. Due to the anti king constraint it rules out 6s in r789c4 and Leaves 1/2/7/8/9 as options for the white dot in r8c89.
12. Together with the dots in r8c123t this creates a virtual pair on 1/2 and on 8 in the row.
13. Now there are several ways to reduce options further in box 7 and 8.
    In particular in cells r9c3 and r9c4. One of them is that r8c4 is 7/9 (can’t be 1 because of the virtual 1/2 pair in the row) and r9c4 is 7/9 (analog virtual pair in the box between the three white dots and the white dot between r9c12). Together they are ruling out 7/9 from r9c3 which becomes a 1.
14. The rest is sudoku utilising the king constraint, one logic path is to ...
15. ... start with row 6 (where does 1 go?), now you can fully resolve …
16. … column 3. Further: Where can 1 go in column 7?
17. Only in r5c7. Now you can fully resolve …
18. … row 6. Further: Resolving the white dot in r3c12 …
19. … brings a naked single row 3 and then
20. in box 1 there is another naked single, now you can finish …
21. column 2 and the rest is trivial.