Sums and Differences
(Published on 18. June 2026, 22:42 by alarark50)
Click here for the video solution by Cracking The Cryptic
Standard 9x9 Sudoku rules apply.
Sums and differences: Along each navy line, starting from the ends marked with a circle, every nth cell is the sum of its two immediately adjacent cells that are on the line. Every mth cell is the difference between its two immediately adjacent cells that are on the line. There is at least one nth and one mth cell on each line, the values of which must be deciphered by the solver. The values n and m are the same for each line.
Thermometers: Digits along a thermometer must increase from bulb to tip.
Kropki dots: Digits separated by a black dot must have a 2:1 ratio.
Little killer sums: Numbers outside the grid indicate the sum of the digits along the indicated diagonal.
No negative constraints. Digits may repeat on constraints if allowed by other rules.
Link to Sudokupad: Sudokupad
Solution code: Please enter row 9 from the left to the right.
Comments
yesterday, 00:37 by alarark50
added link to video solution
on 9. July 2026, 11:48 by QuiltyAsCharged
Fun puzzle with a clear and logical solve path! Unfortunately it seems to have gotten bogged down by a rather silly rules discussion, but don't let that deter you from giving it a go.
>lovely comment, thanks :)
on 7. July 2026, 04:39 by MikeMeech
Great puzzle! The wording of the rules is perfectly clear and made for some fun logic.
>Thanks, so happy to hear that :)
on 30. June 2026, 21:13 by alarark50
changed difficulty due to relatively low solve rate
on 24. June 2026, 18:45 by alarark50
To VitP and anyone else interested:
I sent a reply to VitP's video explaining myself. I suggest you attempt the puzzle first if you haven't, before looking at the discussion, because there are spoilers.
The issue seems to be related to from where the counting starts, not related to the logic behind the puzzle
on 22. June 2026, 15:18 by VitP
I have posted a more detailed explanation on my youtube channel here :
https://youtu.be/XEO8aByCTaY
the explanation is TEXT, in the video description field.
alarark, or anyone else who wishes to, can go there and leave comments.
after resolution, i will be deleting the video.
on 19. June 2026, 23:42 by Sotiris6V
Absolutely no logic error. In fact figuring out m and n is the easier part of the puzzle. Figuring out which is which is slightly harder.
>Thanks, hope you liked this one. I'm working on more puzzles with similar logic
on 19. June 2026, 16:51 by alarark50
thanks for the nice comment, Rocinante :)
on 19. June 2026, 15:05 by Rocinante
Confirmed - there are no logic errors. There is no overlap in the solution. Figuring out the correct n and m is part of the puzzle. No cheating necessary. :)
on 19. June 2026, 11:06 by alarark50
hello VitP. thanks a lot for the comment. I have not figured out how to reply to comments yet, but there is no forced overlap. the short line doesn't strictly require (m,n) = (2,3) or (3,4). I sent the puzzle to some friends for a peer review before uploading and they were able to solve and didn't mention a problem. Of course, that doesn't mean nothing slipped through. Can you walk me through the contradictions and issues you've faced please, if not on here, then at least via mail? You're correct about dark lines, I should change it some time.
on 19. June 2026, 02:02 by VitP
looks like a logic error here.
if EVERY nth cell AND every mth cell follow the rule either a+b=c, or |a-b|=c, then there MAY NOT be any overlap.
short line requires (m,n) = (2,3) or (3,4).
so there will be overlap.
detailed study (by cheating) finds specific contradictions.
also, wide dark lines means candidates and even digits are invisible.
