Easy Peasy Sudoku Advent (17) - Sum and product killer
(Published on 17. December 2025, 06:00 by Richard)
This sudoku advent calendar contains 24 variants that were included in my Sudoku Variants Series (SVS) but turned out to be too hard to be solved by a wide range of puzzlers. I aim for difficulties of 1-2 stars and have written some general and/or specific hints as well. I hope some players will try the original SVS puzzle #418 after solving the advent version.
Sum and product killer
General hint for this type:
If you multiply a digit with 1, the product is one lower than if you add the digit and one. 1x9 = 9, 1+9 = 10; 1x5 = 5, 1+5 = 6 etc. So there is room for a cage total lower than normal with killer sudokus. If there is no 1 involved in the multiplication, there is quickly a high outcome.
In box 1 the cage of 5 is forced to have digits 1,2,3. After that, the cage of 26 can also only have one combination of digits: 4,5,6. Now the minimum for R3C3 is 7, and that can only be derived by multiplying with 1 and adding 2.
Apply classic sudoku rules.
The small numbers in the upper left corner of each cage (dotted outlined region) indicate the sum of the digits in that cage. An X between cells indicates that the two adjacent digits are multiplied when calculating the cage total. (For example: 14 can be formed by the digits 4x3+2 or 9x1+5.) Within each cage all digits must be different.
The remaining digits in box 1 can be filled in, and after that the 10-cage in block 5 is the place to look.
Solution code: Column 9
Comments
on 28. December 2025, 10:52 by TeddieMilo
It looks difficult at first.. once u get one cage, the rest will slowly surface.
on 23. December 2025, 12:22 by Tws
Einfach und schön! Vielen Dank!
on 19. December 2025, 11:41 by SennyK
Nice and smooth, thank you!
on 18. December 2025, 02:15 by SanFranSam
I am going to agree with VitP. Especially with respect to solution checking. Spent 30 minutes reaching a dead end. Wasn't going to start over again because i couldn't find my mistake
on 18. December 2025, 00:19 by damo_89
Very enjoyable. Solve time suggests 1* though I am very good at factoring in my head :D
on 17. December 2025, 22:04 by RandallPepperidge
Marvelous!
on 17. December 2025, 21:47 by michael_787
In my solve, the 25 cage in box 9 was not needed. Definitely 1*: The break-in is obvious, and the puzzle guides you from there.
on 17. December 2025, 20:01 by Klausku
Nice and easy. Thanks!
on 17. December 2025, 19:12 by dzamie
The weird capslock commenter is weird. This is definitely on the harder side of 1*s, I think, but most of the difficulty is in figuring out the possible cage sets, rather than logical elimination patterns. If you know your times tables, this is only a little harder than a standard killer sudoku with just as much cage coverage - pretty easy but not trivial.
I remember getting scared off by the harder version of the puzzle earlier this year; I'll have to give it another go later today, I think!
on 17. December 2025, 16:35 by HeyItsErin
Delightful little puzzle with a rule I’ve never encountered with cages. I would love to see more like this!
on 17. December 2025, 15:10 by VitP
the english version of the rules is incorrect. the german version is CORRECT, but not GOOD. (german "vor" does not match english "when")
sample wording:
small clue indicates the sum of TERMS (addends). an X (in a cage domino) means that its DIGITS must be multiplied to produce a TERM to be summed.
on 17. December 2025, 14:56 by VitP
4 factors which COMBINE to show this is not a level 1 puzzle.
1) a completely UNIQUE ruleset
2) the setter felt the need to provide detailed hints.
3) solution checker not available, meaning solver can't run tests with solving puzzle fully.
4) solver needs to be able to do basic sums and products quickly and reliably, which the vast majority of people CANNOT do. sudoku fans are better than that, but still ...
4a) solver needs to KNOW all the basic cage combinations for a comfortable solve
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Reply: thanks for your solve and taking the time to share your thoughts. May I suggest you add something positive as well?
on 17. December 2025, 14:40 by JVA
Nice nw rule
on 17. December 2025, 11:31 by anothermember
Never encountered this rule before, it's nice. Lovely smooth solve.
on 17. December 2025, 07:52 by Piatato
Smooth and fun!
on 17. December 2025, 07:27 by RandallPepperidge
Marvelous!
