A Strange Property of Anti-Long-Knights Sudoku
(Published on 28. October 2025, 18:15 by RailMan)
Normal Sudoku Rules apply. Place the digits 1 - 9 once in every row, column and box.
Quads: Digits in a circle must appear in a cell touching the circle.
Arrows: Digits on an arrow must sum to the value in the attached circle.
Little Killers: Numbers outside the grid show the sum of the digits in the direction of the small arrows.
Anti-Long-Knights: Digits separated by a Long Knights move (3 squares horizontally and 1 square vertically, or 3 squares vertically and 1 square horizontally) cannot contain the same digit.
As the title suggests, there is something unexpected to discover in this puzzle. Have fun!
Solve Online : Solution Check is enabled
Solution code: Row 9
Comments
on 22. November 2025, 04:24 by TheJRMY
Ok, yes, that IS interesting. And strange. Hmm
RailMan: Thanks.
on 22. November 2025, 04:23 by TheJRMY
I solved this using your clue and a bit of guessing. Looked up Phistomofel’s ring, so now I’m going to try it again in light of that. Seems like it will be very helpful.
on 31. October 2025, 16:16 by RailMan
RailMan: Warning! Spoilers below! If you want to solve the puzzle for yourself then stop reading here.
The idea of this puzzle was to see how an Anti-Long-Knights constraint would work if there was a digit not on the "Phistomofel Ring". PotatoHead21 has looked at a similar idea with an Anti-Knight rule (There are videos on YouTube about it).
An Anti-Long-Knight rule interacts similarly with the Phistomofel Ring, such that any digit not on the Phistomofel Ring must be in the centre of the grid (R5C5). But it is even more restrictive because there are only 2 possible patterns for that digit in the whole grid (and these are just mirror images of each other).
In this puzzle it is possible to show that the 5 is not on the Phistomofel Ring, and must therefore appear in R5C5 and also twice on each of the Little Killer Clues.
From there you can use the arrows to determine which pattern is correct.
I hope you enjoyed the puzzle.
