Sorry, That Sum Is Taken
(Published on 29. December 2025, 18:47 by PhoenixAki)
This puzzle was originally made as a gift for fellow setter sujoyku for a Secret Santa event in December 2025. They have graciously given me permission to post the puzzle as a standalone release here now, which I'm excited to do! This may be my favorite puzzle I've set so far, because I was in quite over my head with the concept at first, but I managed to make it work with a solve path that feels very natural and elegant.
- Normal sudoku rules apply. Place the digits 1-9 in each row, column, and 3x3 box without repetition.
- Killer Cages: Digits in dotted-line cages must sum to the number in the top left corner of the cage, if given. In this puzzle, some totals are entirely ambiguous, and some are given as strict inequalities. For example, a cage that says "> 35" in its top left would have a sum higher than 35 (and not 35 itself).
- Region Sum Lines: Box borders split blue lines into sections, and the digits on those sections must sum to the same value.
- Sum Uniqueness: Each sum can appear at most once in the puzzle. This rule applies to killer cages and region sum lines. For example, if a region sum line is determined to have its segments sum to 6, no other line can do the same, and no cages may sum to 6.
- Kropki Pairs: Digits separated by a black dot must have one digit be double the other (a 2:1 ratio). Digits separated by a white dot must be consecutive.
To increase accessibility to my puzzles, I include hints in my puzzle posts (see below). I also post solution videos on my Patreon and YouTube channel. Puzzles released prior to February 2026, as well as my snackdoku and variant sudoku 101 series will continue to get public solution videos on YouTube, while others will be Patreon-exclusive.
Hint 1: 2-cell cages have a maximum sum of 17. 5-cell region sum lines have a minimum sum of 15. These facts are very important for the break-in.
Hint 2: Once you've identified a few sums via hint 1, follow it up by checking the other cage totals. Knowing they can't include the first few sums you identified makes them more restricted. Do this enough and you'll eventually have enough info in column 1 to work out the region sum line.
Hint 3: What purpose could R1C9 being in a single-cell cage have for the puzzle? Where can that digit go in box 5?
Hint 4: Pay special attention to the 2-cell sum line segment in box 6. There's a digit that must appear on it that will tell you what that line's sum must be.
Hint 5: The final disambiguation step requires 2 things. First, you must have classic sudoku worked out enough to know what R7C2 is. Second, you need to factor in the sums of the non-totaled cages in boxes 3 and 9. Combine it all together and you'll be done!
Solution code: box 1 in normal reading order (left to right, top to bottom). 9 digits.
Comments
on 7. February 2026, 19:00 by Lor
Solving this was fun. I only read the hints after solving, but still want to thank you for making the effort to include them. It's not easy to create good hints that still leave the solver able to enjoy the puzzle with a little help.
on 28. January 2026, 01:27 by PhoenixAki
Added links to Patreon.
on 14. January 2026, 10:17 by PhoenixAki
Added hints after learning recently how to do that in HTML. Wish I knew this last week when I went over all my posts...oh well.
on 9. January 2026, 01:18 by PancakePie
Once the flow started, it was an extremely fun path through this gem! Thank you for making this beauty!
on 8. January 2026, 20:55 by pmakholm
Wonderful.
I felt I had mad good use of the unique sum and then I got stuck, convinced that a specific pair would be the key deduction. After an hour of bifurcation I realized that it was trivial to resolve using unique sum. Even Simon would be yelling at me at that point...
Oh well, it was treat.
on 6. January 2026, 13:52 by jez9999
Loved this puzzle, not too easy, not too hard, quite smooth solve path!
on 6. January 2026, 05:52 by PhoenixAki
Updated post as part of an effort to improve consistency of rule phrasing and post layout across all my puzzles.
on 3. January 2026, 08:21 by GinaT86
Brilliant puzzle, really enjoyed the sum uniqueness!
And I love your consideration having the YouTube solves (and accessible link text) :) I'm doing more of your puzzles for sure and look forward to a few trickier ones perhaps one day!
on 30. December 2025, 23:15 by Qodec
Very clever!
on 30. December 2025, 21:23 by s1mn
Fantastic puzzle! I really enjoyed it, thanks.
on 30. December 2025, 19:24 by harwiltz
This was a blast! Especially once I noticed that not all inequalities point in the same direction :D
on 30. December 2025, 18:30 by rojspencer
Loved it!
on 30. December 2025, 14:49 by sujoyku
Thanks again for this wonderful gift, PhoenixAki!
This has been such a joy to solve.
on 30. December 2025, 11:14 by Fizz
Very clever and fun puzzle, thanks!
on 29. December 2025, 19:56 by tallcat
Very enjoyable and a smooth solve path!
on 29. December 2025, 19:39 by wuc
Very smooth. Didnt catch that cages anf lines interact on uniqueness first. From there very nice approachable. Great fun thx.
on 29. December 2025, 19:30 by HeyItsErin
Really fun puzzle! I can see why it’s one of your favorites.
on 29. December 2025, 19:05 by SennyK
Fun and clever easy puzzle!
