Easy Miracle
(Published on 31. May 2026, 19:34 by addie)
Antiknight and Antiking: Any two cells separated by a knight's or king’s move in chess cannot contain the same digit.
Nonconsecutive: Any two orthogonally adjacent cells cannot contain consecutive digits.
Ratio Kropki Dots: Digits separated by a black dot have a 2:1 ratio. Not all dots are necessary given.
XV: Digits separated by an X sum to 10, those separated by a V sum to 5. Not all Xs and Vs are necessarily given.
Solution code: Row 1
Comments
on 22. June 2026, 14:41 by superkinkel
Oh my god, I struggled with this one so much. I spent ages focussing on disambiguating the potential Kropki pairs, when actually the question were the 1 can and cannot go, makes this a easy as it could be.
on 13. June 2026, 07:39 by VitP
there IS an "easy" solution if you know your way around these variants. it does not require serious bifurcation, or grid-wide colouring.
1) 1-2 black kropki is illegal.
1a) therefore, there are TWO flavours of black kropki, 3-6 & 4-(2/8)
2) start in a box with 2 black kropkis, eg. 9. assume one configuration, & track the colours around the grid. there is a problem on row 1.
3) this gets you the 4s, and then the 3-6s pairs follow directly, and then the rest just flows in like water.
super easy for experts. likely out of reach of beginners.
on 13. June 2026, 07:28 by VitP
this is NOT level 2.
it requires either
a) a priori knowledge of the grid-wide miracle structure, not common knowledge
b) working it out from scratch
on 8. June 2026, 12:01 by KingIsulgard
21 minutes for me. But without knowing about the consequences of this ruleset, with regular brute force coloring, this would be a 4 star imho.
on 2. June 2026, 20:02 by addie
JVA, okay thank you for trying it!
on 2. June 2026, 17:12 by JVA
I do appreciate the help, really, but I'm giving up on this puzzle. It's beyond me.
on 2. June 2026, 00:19 by addie
To anyone who doesn't want a hint/spoilers, don't read this comment!
To JVA: Here is a method that might help you start if you want a more specific hint. Try bifurcation on the V pair again. Since one of the two cells in the V pair will be a 1, test them both. Using the antiknight, antiking, and nonconsecutive rules (meaning there can be no 1 in any kropki pair), you should be able to determine which cell in the V pair is the 1. From there you should be able to find all the 1s.
That should help you get started, if you want the next step let me know!
on 1. June 2026, 19:59 by addie
JVA, have you tried bifurcation? I know it's controversial, but personally I use it a lot because I don't know many strategies/rules. It would definitely help with this puzzle!
on 1. June 2026, 18:54 by JVA
Coloring has gotten me nowhere, because there's three flavours (2*4, 4*8, 3*6).
I think I'm just going to give up on this one, if the hints are the same strats I've already tried and failed at, that probably means the puzzle is too difficult for my level
on 1. June 2026, 18:41 by itsid
that's been easy.. I stared at the endgame for a while until I realised that 7 not only is next to eight, it's alöso next to six... sometimes I swear I have a brain tumor *duh*
JVA: color the grid first,
and I bet you know there are two flavours of black kropki pairs.. so label them as well..
with that and colours you will most certainly notice which label is what flavour and you can go from there
on 1. June 2026, 18:11 by JVA
That's what I've been trying to do for half an hour, but there's 3 potential combinations for the dots and I don't see a way to restrict any of them
on 1. June 2026, 15:57 by addie
JVA, focus on the combination of the nonconsecutive rule and the kropki dots!
on 1. June 2026, 15:49 by JVA
I'm finding this way, way, way harder than any other antiknight + antiking + sudoku I've done, any hints for the break?
on 1. June 2026, 01:16 by tuberculosis
Very nice. Took me a bit to crack the first digits but went quickly after that.
on 1. June 2026, 00:48 by addie
Myfyr MJ, not all black dots are necessarily given. Thanks for pointing that out, I made the rules clearer!
on 1. June 2026, 00:47 by addie
Rule clarification
on 31. May 2026, 22:39 by Myfyr MJ
As all white dots are given (none), are all black dots given or not? Can you clarify the rules? Thanks.
on 31. May 2026, 21:29 by Mizuki
Fun!
on 31. May 2026, 19:44 by addie
Image
on 31. May 2026, 19:43 by addie
Fixed rules
on 31. May 2026, 19:41 by addie
Added image
