## The S-Cell Miracle

(Eingestellt am 22. Mai 2022, 16:40 Uhr von Niverio)

After solving Region Geometry by kolot, I have been busy trying out his challenge, where he challenged people to set a Chaos Construction puzzle with only ? outside clues. And after countless failed grids, I abandoned the Chaos Construction part and decided to try out the idea in a regular Sudoku grid, since I really believed in the potential of the puzzle and the ruleset. And after even more broken grids, here I am with a miraculous looking grid. I hope you enjoy, although be warned, this puzzle is extremely difficult.

-Normalish Sudoku rules apply. Place the digits 0-9 in the grid so that every row, column, and 3x3 box contains every digit exactly once. To enable this, there is a single Schrödinger cell in each row, column and box, containing a superposition of two different digits.

- When there is an arrow outside of the grid, that indicated row/column's X-Sum clue (The sum of the first N cells, where N is the total of digits in the first cell seen in that direction.) is equal to the sum of the digits in that row/column's S-cell.
-For the diagonal clues this rule applies diagonally in the indicated direction. If a diagonal has more than one S-cell, the clue applies to the first seen S-cell. A diagonal clue can be a 0 if the indicated diagonal has no S-cells. The clues to the right of R7C9 do not affect each other.

Puzzle Links: Solve in Penpa with answer check or solve in the CTC Software

Lösungscode: Write in the contents of Row 5 followed by Row 6. Write the contents of the S-cells with smaller digit first. Total of 20 digits, no commas or spaces.

Zuletzt geändert am 24. Mai 2022, 01:24 Uhr

Gelöst von Jay Dyer, Siebuhh, kolot, the_cogito, bigger, marcmees, JayForty, ancarro, Jesper, wenchang, hepcecob, amarins, polar, starwarigami, Xenonetix, purpl, XYX, tinounou, henrypijames, Gliperal, Vebby, cdwg2000, Christounet
Komplette Liste

### Kommentare

am 17. Juni 2022, 10:45 Uhr von Christounet
Wow, that was extraordinary ! Did not think that you could combine S-cells with question mark clues only... Guess I was wrong... I tried it a couple weeks ago but I repeatedly hit a dead end because of the first formulation of the rules which did not precisely stipulate that the row and diagonal clues in front of R7C9 could be different ! As I am fond of S-cells, I decided to come back to it today and saw that you had clarified this rule ! Wonderful solve nonetheless !!

am 6. Juni 2022, 23:02 Uhr von Vebby
Wow, brilliant construction! One tough knot to unravel in the mid-solve after which it resolves beautifully.

Zuletzt geändert am 30. Mai 2022, 23:18 Uhr

am 30. Mai 2022, 22:37 Uhr von henrypijames
There are a few spots in my solve where the logic is so complex it borders on bifurcation. Don't know if I missed simpler paths, or is it supposed to be this difficult.

Most of the 5 difficulty rated (LMD consensus) puzzles I've solved recently have actually been 4 for me, but this one is 4⅔.

~The puzzle IS difficult, but no specific step should be so brutal that you would need to bifurcate through it. You probably missed one such step that made the upcoming steps harder. Still, thank you for persevering!

am 24. Mai 2022, 18:12 Uhr von hepcecob
Wow was this difficult, so many places to make mistakes, but the logic is amazing. Had a great time, but had to restart several times due to wrong leap in logic.

Zuletzt geändert am 24. Mai 2022, 17:56 Uhr

am 24. Mai 2022, 17:45 Uhr von wenchang
Very hard puzzle, but it is excellent!

https://youtu.be/3xisplcI-WU

am 24. Mai 2022, 15:51 Uhr von Jesper
Great puzzle! I found it properly challenging; very rewarding to find all the deductions and finish the solve!

am 24. Mai 2022, 01:24 Uhr von Niverio
Updated the CTC link after seeing that Mac users were having trouble with arrow symbols. Mobile can still have such issues, if you are attempting on mobile either use Penpa, or just solve normally since the symbols are only placeholders for the ruleset anyway.

am 24. Mai 2022, 01:03 Uhr von Niverio
Updated the puzzle image, and thus it's links accordingly following bigger's suggestion.

am 23. Mai 2022, 22:51 Uhr von marcmees
it helped. very nice solve. hard but fair.

Zuletzt geändert am 24. Mai 2022, 01:04 Uhr

am 23. Mai 2022, 21:54 Uhr von bigger
one small advice, if you want to have only one type of clues, try using arrows.? has only one direction but arrow has three. the red ? could be replaced with two arrows pointing left and top left. but if you insist using all ?, I guess coloring is the best solution.

~ Thank you for the suggestion, it indeed looks clearer now. It also spared some room in rules.

am 23. Mai 2022, 16:50 Uhr von the_cogito
Loved this puzzle, tricky beginning, but a nice flow and really clean and fun deductions throughout

am 23. Mai 2022, 15:17 Uhr von Niverio
Rule clarification.

Zuletzt geändert am 23. Mai 2022, 10:17 Uhr

am 23. Mai 2022, 10:09 Uhr von Briks
A question on the red clue:
It belongs (horizontally) to the row starting in c9/r7, diagonally it starts in c9/r6?

~Yep, that is correct.

Zuletzt geändert am 23. Mai 2022, 10:17 Uhr

am 23. Mai 2022, 09:00 Uhr von kolot
The difficulty of this puzzle is solid 5 stars but it is not a monster I think. There are some interesting and unusual logic on the path. Well done!

~Thank you so much for the kind words!

Zuletzt geändert am 22. Mai 2022, 22:07 Uhr

am 22. Mai 2022, 21:16 Uhr von Siebuhh
Nice puzzle! We assumed that the first cell next to a ?-clue can not be a S-cell

~It actually could be! But the only possibility is a 01 S-Cell, and in this iteration that instance never occurs :)

 Schwierigkeit: Bewertung: 99 % Gelöst: 23 mal Beobachtet: 1 mal ID: 0009ZT

Lösungscode: