Easy Peasy Sudoku Advent (21) - Cage Relations
(Published on 21. 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 #445 after solving the advent version.
Cage Relations
Specific hint for this puzzle:
If the first cell in a row or column is a one-cell cage, followed by a black diamond, the sum of the second cage is the square of the first digit.
Apply classic sudoku rules.
Digits in cages may not be repeated. Each cage has a sum that can be derived by adding all the digits it contains. A diamond between two cages indicates that their sums have a difference (white diamond) or a ratio (black diamond) that is equal to the topmost (in case of a column) or leftmost (in case of a row) digit of the column or row in which the diamond is placed. All possible diamonds are given.
The cage in R45C2 cannot be the first digit to the power of three of the top cage, but must be the same as the single cell cage in R1C2.
For this type it is very important not to rule out possible cage totals too soon. A cage can have a smaller or larger sum than it’s neighbour, but can also have a positive or a negative ratio with it’s neighbour!
A 1 in the first cell of a row/column indicates that two neighbouring cages have the same sum in case of a black diamond, or a difference of 1 in case of a white one.
Sudokupad (no answer check)
Sudokupad (with answer check)
or
Penpa+. There is a white diamond missing in C5 between R2 and R3. Currently working on it.
Solution code: Column 7
Comments
on 23. December 2025, 00:50 by dzamie
Ooh, I remember the harder version of this - I might try to solve it a second time sometime.
This one opened up a lot faster! As others have noted, it's solvable without the negative constraint, which I think probably provides some extra challenge, since doing so means not crossing off potential sums as early.
on 22. December 2025, 05:49 by nyxie
This was very fun! I did not need the negative constraint at any point FYI.
on 22. December 2025, 04:39 by zembrost
a fun variant, thanks!
on 21. December 2025, 15:08 by Karitsu
Maybe I just got lucky, but this was an easy 1* for me. Took about half the time most 1* puzzles usually takes me. Interesting and fun new (or at least new to me) rule!
on 21. December 2025, 14:36 by Franjo
I already had solved the original, a fantastic one, but this again is a perfect appetizer! Thank you very much for creating and sharing this lovely puzzle.
on 21. December 2025, 14:32 by wuc
Smooth approachable 2* puzzle. Great setting thx.
on 21. December 2025, 12:53 by Klausku
Nice and easy solve. Thanks.
By the way: the german phrasing is correct.
on 21. December 2025, 11:53 by SennyK
Another lovely puzzle! I do not know whether you have already amended the english wording or not, but it is very clear the way it is now :-)
on 21. December 2025, 10:22 by Piatato
Very nice and smooth, thanks!
on 21. December 2025, 08:05 by henrypijames
The rules are very hard to comprehend - there are simply too many "or" in the sentence, and mentally constructing a boolean tree for those "or" is too much. It'd be much better to just state the case for a white dot in a row, then say that the black dot works the same except … , and a dot in a column works the same except …
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Reply: thanks for your valuable feedback. I can give rephrasing a try for the English version, but since I am not a German, I can't do this for the German version.
on 21. December 2025, 07:57 by Richard
Fixed a missing diamond in C5 between R2 and R3. Still working on the Penpa link.
Sorry for the inconvenience and thanks r45 for pointing out!
Incredible that this slipped through after thorougly checking...
