Anti-Kropki Cages
(Published on 7. August 2025, 07:31 by marty_sears)
Happy birthday to Justin Vitanza, AKA Vitaminz. We once set a puzzle together called Chock-a-Block, in which we came up with a constraint called the Anti-Kropki line. Here I have developed the idea in a way which I hope will bring some joy to the great man on his birthday.
Normal sudoku rules apply.
No two digits ANYWHERE in the same cage may be consecutive, OR in a 1:2 ratio, but they may be the same.
Every cell in the grid is in a cage! (Some cages are invisible, and their shapes must be discovered.) Cages all have at least two cells, and don't overlap. A digit in a circle indicates the size of its cage.
Please leave a comment if you enjoy :)
Solution code: Row 9 from left to right
Comments
on 4. September 2025, 23:20 by KelleyCook
Very interesting, once I got the fist few anti-kropki cages I thought this was going to be easy.
But its Marty Sears, so it turned out to not be easy at all; getting all the cages to match the circles was quite tricky.
on 3. September 2025, 16:54 by Danno
Wow what a puzzle. So satisfying working through the logic and seeing it all unravel. A tough puzzle but definitely worth solving. Amazing job mate
on 27. August 2025, 05:31 by Bankey
Tough but great fun. Thanks, @ marty_sears :).
on 15. August 2025, 13:44 by Nairurian
It was definitely on the more challenging side of 3*, possibly 3,5*, but a very enjoyable puzzle one I got my brain to work with the constraints.
on 11. August 2025, 20:59 by davidz32z
Really tough one, but a delightful struggle!
on 11. August 2025, 20:44 by virus_dave
I found this closer to 3.5* for me. Quite tricky at times, especially considering the novelty of the constraints (to me, at least)
on 9. August 2025, 10:42 by polcat
Wonderful puzzle! Thank you.
on 9. August 2025, 08:05 by Exigus
Very cool. Thanks!
on 8. August 2025, 23:58 by cozmic72
Whoa, what a puzzle. For me this was pretty hard - like others here, it took me a while to master the constraint, but it was rather satisfying when it clicked and I got unstuck. Great as ever, Marty!
on 8. August 2025, 18:47 by jakestilesowen
Very clean puzzle with fun logic. Thanks for it!
on 8. August 2025, 06:27 by mse326
Guys 2 hours into this I made an amazing discovery that could revolutionize math let alone sudoku...8 is consecutive with 9
on 8. August 2025, 03:20 by juggler
Great puzzle, very streamlined rules as well!
on 8. August 2025, 03:20 by Crusader175
Lovely!
on 8. August 2025, 01:30 by RedBarchetta
I too thought impossible until I understood the "ANYWHERE" comment. Very cool puzzle. I kept breaking rules, like assigning random cells as a "circle" cell, or randomly ending a cage length. Definitely had to be cognizant of the rule set. But quite approachable once I got it. Thanks!
on 7. August 2025, 20:26 by polcat
Wonderful puzzle! Thank you.
on 7. August 2025, 15:06 by Franjo
Took me a while to master these Nabner+ cages! (I gave 4*.) This puzzle cooked my brain, but in the end I was completely satisfied. Thank you very much for creating and sharing another lovely masterpiece.
on 7. August 2025, 14:44 by vitaminz
Such kind words and an amazingly satisfying puzzle. What a beautiful present, thank you!
on 7. August 2025, 11:15 by mscha
Nice! At first glance, seemingly impossible, but then you see a way forward and it's not so bad at all..
on 7. August 2025, 11:14 by Asparagus
Great fun!
on 7. August 2025, 10:26 by Dermerlin
For me this felt like 3-4 stars.
Nice puzzle anyway.
on 7. August 2025, 10:12 by StefanSch
Nice logic!
on 7. August 2025, 08:23 by sanabas
trickier than it looks
