Schrödinger Lines Pt.2
(Published on 20. March 2025, 15:11 by Zanno)
Ever wondered what happens when a line follows several rules at once? Get ready for some weird interactions...
Play on SudokuPad
Rules
Normal Sudoku rules apply. (Place the digits 1-9 exactly once in each row, column, and 3×3 box.)
Each 3×3 box imposes a unique rule (from the list below) on all lines that pass through it.
A line must follow the rule of every box it enters for its entire length, not just within that box.
A line does not follow the rules of boxes it does not enter.
(e.g., On a line that never enters the "Whisper" box there is at least one instance, where adjacent digits differ by less than 5)
The nine rules:
Entropy: Every set of three consecutive digits must include one digit from {1,2,3}, one from {4,5,6}, and one from {7,8,9}.
German Whisper: Adjacent digits differ by at least 5.
Modular: Every set of three consecutive digits must include one digit from {1,4,7}, one from {2,5,8}, and one from {3,6,9}.
Nabner: No two adjacent digits are consecutive, and no digit repeats.
Palindrome: The digits on the line read the same forward and backward.
Parity: Adjacent digits alternate between odd and even.
Region Sum: The sum of the digits on the line is the same in every 3×3 box it passes through.
Renban: The line contains a set of consecutive digits (not necessarily in order).
Zipper: The sum of each pair of digits equidistant from the central cell of the line equals the digit in the central cell.
Solution code: Row 9
Comments
on 8. April 2025, 13:33 by Niverio
Wow, what a puzzle :) I thought the puzzle would get easier after determining most of the box constraints (or at least pairing them to 2 boxes), but I was wrong. That mid solve is absolutely ruthless, but it makes it just that much more rewarding when you see how the (negative) constraints impact certain areas of the puzzle!
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Thank you for solving and commenting! Glad, you enjoyed it.
And yes, that negative constraint... the setting process was a constant juggle between using it for the solve-path and avoid letting it break the puzzle ;)
on 1. April 2025, 14:13 by skuntsel
This is an incredible and a very clever puzzle! To me it felt like a younger sibling of Niverio’s Dynamic duos classic. A very natural feel to the solving and the puzzle doesn’t give up literally until the very end. Just incredible how this all resolves given the minimalistic grid. Very nice interplay between the lines and tension arising from seemingly tiny things. Three-to-four length lines that are ambiguous and meaningful? No, this must be a joke. Thank you, Zanno, it was a few hours of pure joy, you came up with an astonishing setting!
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Thank you for your high praise! I did really enjoy setting it and I'm happy you had so much fun solving it.
And thank you for pointing me to Niverio's Puzzle! I didnt know any other puzzles with this type of "double-constraint" and I cant wait tackling Niverio's take on it.
on 24. March 2025, 17:12 by Zanno
@askaksaksask: Thank you for your kind words! I'm glad you enjoyed it.
@Da Letter El: Thank you to!
on 21. March 2025, 21:00 by askaksaksask
Incredible. This was properly difficult, I found, but so rewarding. A true setting wonder, that the only real "tell" here is the line geometry. Those lines spanning four boxes are truly inspired. You'd think the negative restrictions would make the interactions easier, but oh my, not so. What a brilliant work. Thank you for this!!
on 20. March 2025, 18:07 by Zanno
Yes, zippers must be of odd length.
on 20. March 2025, 17:58 by Da Letter El
the way zipper rules are written here, it implies that there cannot ever be an even length zipper line. is this intended?
edit: lol i got beaten to it
on 20. March 2025, 17:57 by henrypijames
This definition of zipper line seems to rule out even-length lines from being zipper from the start - is this correct?
