SET Equivalence Theory
(Published on 5. September 2022, 00:21 by tesseralis)
I've been wanting to make a sudoku based on the card game SET for some time. Entropy and modularity feel like natural ways to implement it, and I think the resulting interactions provide some fascinating logic.
Rules
Normal sudoku rules apply.
Digits along a blue line sum to the same value in each box it passes through.
Let a digit's entropy describe if it is low (123), medium (456), or high (789). Let its modularity be its remainder when divided by 3.
Let a SET be a set of three digits such that their entropy and modularity are either all the same or all different. Some examples of SETs are: 789 (same entropy, different modularity), 258 (different entropy, same modularity), 168 and 348 (different entropy and different modularity).
In this puzzle, the three rows and three columns of each box all form SETs.
Solution code: Column 5, then row 9
Comments
on 16. November 2023, 18:03 by The Book Wyrm
Nice puzzle!
A cool and unique ruleset with some interesting properties to figure out, and you made very good use of it. Interacts well with the region sum lines.
on 16. November 2023, 08:21 by zzw
Wow, this was incredible! I don't often do puzzles with global constraints like this, but this sounded intriguing enough to try, and I'm really glad I did. The SET rule interacted very well with the region sum lines. Had to do a lot of thinking to even get started, and then later got stuck for a while and had to do a lot more thinking, but it all resolved in a very beautiful way. Highly recommended!
--
Haha! I didn't think you'd actually do the puzz XD. much appreciated, and thank you for the kind words! ~tess
on 10. August 2023, 08:57 by Christounet
Really interesting puzzle ! It made me discover some really surprising property of one of the SETs. Well, it is not that surprising when you start thinking carefully about it. But it still surprised me that it could be the basis of a puzzle. The end felt a bit trickier than the rest of the puzzle, like I knew what was gonna happen, but I had a hard time finding the logical proof without bifurcating ! But I did it and enjoyed it !
Note for future solvers : in box 5, there are TWO diagonal region sum lines crossing in R5C5, it is NOT a single RSL !
on 5. September 2022, 00:52 by tesseralis
Change formatting.
on 5. September 2022, 00:51 by tesseralis
Change formatting.
