Ne Plus Ultra
(Published on 3. February 2022, 08:55 by Andrewsarchus)
A Schrödinger Cell Chaos Construction...
Rules:
- Schrödinger Sudoku rules apply.
- Regions must be determined by the solver.
- Each row, column, and region must contain one complete set of the the digits 0-9 without repeats. To accommodate this, some cells (called 'Schrödinger cells' or 'S-cells') may contain two digits.
- Each row and column in the solved grid must contain exactly one S-cell.
- There is no restriction on how many S-cells a region can contain as long as the region has exactly ten digits.
- Circles contain a digit which counts the number of cells (including themselves) in the surrounding 3x3 neighborhood which belong to the same region as the circled cell. All possible circles are given.
- Squares contain a digit which counts the number of regions (excluding their own region) which have cells in the surrounding 3x3 neighborhood. All possible squares are given.
- In the case of a circle or square on an S-cell, only one of the digits must satisfy the constraint, while the other digit is unconstrained by the circle/square.
- Arrows on the border between cells point to the S-cell in the corresponding row or column, and the digit in the cell at the tail end of the arrow indicates the distance from that cell to the S-cell. The distance must be a positive number. All possible arrows have been given.
- Blue lines are Equal-Region-Sum lines. Each line visits at least two regions, and the sum of all the digits in the cells for each pass through a region must be the same for any given line.
Play Online:
ctc: Ne Plus Ultra
Solution code: Digits in the S-cells
(top to bottom, lower digit first, total of 18 digits, no spaces)
Comments
on 16. February 2024, 22:20 by Myxo
Awesome puzzle, really enjoyed every step!
on 12. November 2022, 11:37 by PrimeWeasel
Yeah.... I mean.... yeah...phew...I did it. What a ride! Highly recommended
on 18. October 2022, 21:33 by zetamath
This is honestly one of my favorite puzzles of the year!
on 18. October 2022, 06:27 by wisty
This puzzle is incredible! The amount of interest and cohesion packed into such dense and often difficult logic is such an inspiration.
on 26. August 2022, 20:06 by Agent
What a puzzle! 5/5 difficulty is an understatement.
on 23. May 2022, 09:05 by DiMono
Almost 3 hours on my solve time. I suppose beginning at midnight was perhaps not the smartest decision I've ever made.
on 21. May 2022, 03:30 by OGRussHood
Madness. Sheer madness.
on 23. March 2022, 01:22 by thefallenrat
It was worth it to spend over 10 hours to complete this absolute beautiful and brutal puzzle. Well done on creating this masterpiece! I look forward on more of your Chaos Construction puzzles!
on 22. March 2022, 15:29 by Jesper
Well, that was... quite difficult. Great puzzle! I half expected it to break when I was finishing up the digits, and I am eternally grateful that it didn't, because I really did not want to troubleshoot my entire solution path :)
on 22. March 2022, 08:57 by MagnusJosefsson
Amazing puzzle! It has a really long and narrow logical solution path and level of difficulty that is high but consistent, only getting easier at the very end. To achieve all this with a ruleset with so many negative restrictions is truly impressive. A very long and difficult puzzle, but incredible satisfying to finish.
on 20. March 2022, 00:21 by Niverio
One of the very few puzzles that I can confidently mark as 6/5 for difficulty. My second longest ever solve, just after Quite a Mouthful. Solving this live in front of Andrew was a joy. He probably has no hairs left because of the mistakes I almost made though. Took 3 hours and 15 minutes at the end.
And yes, agreed with everyone below. Its just insane.
on 16. March 2022, 02:12 by Silverstep
Incredible puzzle. Each deduction step feels surprising and out-of-nowhere like "did I do this? how did that happen?"
It's also amazing that, despite the complicated ruleset:
- The puzzle does not feel like it's divided into "stages". There was no moment of "I have completed this type of clue, yet I have hardly touched this other type of clue at all"
- There was no tiny, out-of-place clue just to disambiguate a few final digits at the end.
All of the clues in this puzzle work so well together and I really enjoyed that.
on 13. March 2022, 18:47 by harrison
Oh my goodness! This might be the most involved puzzle I've ever solved. Never felt impossible but every step was enormously difficult. Hours and hours of "fun".
on 6. March 2022, 09:32 by Andrewsarchus
Rules clarification:
I added the stipulation that the distance to S-cells indicated by the arrow clues must be positive. The question came up several times regarding whether or not it was permitted to have an S-cell immediately behind an arrow in which one of the S-cell digits was a 0 for the distance. This would contradict the "points to" phrase in the rules. Note that the stipulation that the distance is positive also implies that the negative constraint on arrows does not exclude the possibility of an S-cell containing a 0.
I have updated the puzzle link, but for those who have solved the puzzle prior to this update, I am providing the old link here, so that you can still access your solution which the app saves in your local storage.
https://tinyurl.com/2p8ph6tc
And thank you all for your solutions and comments! :-)
on 21. February 2022, 20:39 by ns08
Amazing and insane puzzle! Logic was so hard and beautiful.
on 18. February 2022, 21:25 by henrypijames
What?! How?! A puzzle that overwhelms you with negative constraint - never seen anything like this. Totally agree with the consensus verdict of "insane" - it's a "must be seen to be believed" (and even then just barely) kind of puzzle.
Before I got started, I had commented in another puzzle that equal sums would be a "vicious" constraint in a chaos construction, since you don't know where the borders are. This puzzle not only proves that, but the ES-CC combo doesn't even come close to being the most vicious thing about it.
Naturally, I lost count on how many times I broke it and had to restart - and finally solving it feels like a monumental achievement. This was probably the most amount of brain power I've put in to solve a sudoku - and now I'm total exhausted, in a good way, like after a heavy workout (not that I never do).
Wanna see Simon tackle this one - it might set a new record for video length.
on 15. February 2022, 21:40 by hepcecob
How the hell do you even come up with this? This was insane. There were a couple things that threw me off: if a 0 could be in a Schrodinger cell or not. Granted you don't actually need this rule spelled out to solve the puzzle.
Again amazing, very difficult puzzle.
on 10. February 2022, 16:13 by Chilly
Well, once I realised it was 'each visit' for the equal sum lines (after several days of stubbornly failing :) )it solved very nicely - beautiful puzzle, and very hard - in a good way.
on 4. February 2022, 03:49 by KNT
absolutely insane
on 4. February 2022, 03:00 by starwarigami
This puzzle is insane! But in a good way.
on 3. February 2022, 18:58 by grkles
Considering it took me about 5 (admittedly distracted) hours to solve this, with help from the setter, I think I can confidently mark it 1 star for difficulty.
Incredible, elegant logic. I'm honestly amazed that this works at all, let alone that it works so beautifully.
on 3. February 2022, 14:21 by Andrewsarchus
clarification for solution code
