Mods, Quads, Odds & Schröds
(Published on 17. October 2023, 15:00 by ThePedallingPianist)
Part 1: Mods
Part 2: Mods and Quads
Part 3: Mods, Quads and Odds
Part 4: Mods, Quads, Odds and Schröds
Play on f-puzzles
Play on CTC
Note: for the answer check to work, delete all the 0s from the finished grid.
Fill every row, column and 3x3 box with the digits 0-9 exactly once each.
Schröds: there are 9 Schrödinger cells in the grid, which contain 2 different digits.
Same Difference lines: adjacent digits on a turquoise line must have the same difference, though this difference can be different for different lines.
Quads: each quad circle contains all the digits in the surrounding 4 cells. Unfortunately these quad clues have all been written in white text, and so are invisible. Digits might repeat within a quad circle.
Odds: digits in a grey circle must be odd.
Circles: a digit in a circle (odd or quad clue) shows how many times that digit appears in a circle. E.g. if there is a 5 in a quad clue, then there must be 5 total appearances of 5s in quad clues and odd circles combined.
For the purpose of Same Difference lines, the two Schrödinger digits are considered to be adjacent on the line. For example, 7-(35)-1 would be a valid line, but 7-1-(35) would not.
For the purpose of quad clues and odd clues, the two Schrödinger digits are considered separately; for example, a (35) Schrödinger cell in an odd circle means that 3 and 5 each gain one extra appearance in circles.
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Please remember to leave a comment :)
Solution code: Row 1, left to right (10 digits, Schrödinger cell to be written with the smaller digit first)
Comments
on 15. February 2024, 23:51 by QuiltyAsCharged
Stellar! This puzzle is the perfect conclusion to an amazing series. It is tricky and deserves its 5-star difficulty rating, but don't let that scare you away. If you've completed the rest of the series and you have a little experience with Schrödinger cells, you have the toolset you will need.
on 6. December 2023, 23:14 by Duga
This was the hardest puzzle I have actually solved here. Took me about 6 hours over 2 days. Also my first 5 star :) I absolutely adored the logic in this series. So fun. Hope there will be more puzzles implementing this in the future.
on 5. December 2023, 17:39 by heliopolix
S-tunning puzzle! Early assumptions can lead to sudden dead ends, so double check each one! Once you get going, it flows very nicely all the way to the end!
on 21. November 2023, 00:59 by konklone
Goddamn. That was tough but mesmerizing. I echo the commenters below that you really need to interrogate yourself before concluding that something is broken! Or if it is broken, go back a bit and think harder about your conclusions. The combination of Schrodinger cells and same difference lines is brain-bending, and that's besides the bending of one's brain on the circles themselves!
on 12. November 2023, 13:42 by rich_27
Mods, Quads, Odds, and Schröds is a gift from the Gods; my gods what a beautiful puzzle, a serious contender for my all time favourite. It took me a couple of hours to solve once I'd understood the rules correctly; and many, many hours across multiple days beforehand.
I thought Schrödinger cells considering their digits adjacent on the line meant they spliced two number lines together, meaning you could do something like 7->(9,0)->2, and it created a huge problem space. Realising the digits must have the same difference between them as the difference between adjacent digits on the rest of the line not only made it solvable, but made it feel really intuitive too. I was actually surprised how much of the puzzle you could work with spliced lines!
What an amazing ruleset the Schrödinger cells create! It's such different and fun logic pinning down which cells overlap, and it creates such a beautiful flow through the solve, almost like fog without the fog - anywhere you don't know the location of Schrödinger cell is shrouded in a blanket of possibility.
What a great puzzle, I really hope you do more in the same vein! (Pods? Rods?)
on 11. November 2023, 03:20 by wand
wowee zowee this was awesome. quite hard, but these constraints work magic together.
definitely got stuck at a few points, but there was always something reasonable to find, eventually.
on 8. November 2023, 19:33 by Spyrfyr
If someone is stuck like I was, here is a hint:
[-- Stop reading if you do not desire any hints! --]
This hint clarifies a misunderstanding of the rules that I had:
When I read "For the purpose of quad clues and odd clues, the two Schrödinger digits are considered separately", I mistakenly interpreted it to mean that a Quad can be completed (to contain four digits) using only three cells, if one of the cells is a Schröd.
I thought this interpretation is valid because I thought that the Quad rule did not specify that all surrounding cells touching a Quad must be within the Quad -- I mistakenly thought that the Quad rule only specifies that all digits in the Quad must appear in surrounding cells.
However, in reality the Quad rule clearly says: "each quad circle contains all the digits in the surrounding 4 cells."
on 29. October 2023, 19:12 by mikepautov
This is a beautiful puzzle, it took me some time to make a step away from a false trail ;) Nice series!
on 28. October 2023, 00:40 by pms_headache
OMG this one has vexed me since it was published. I loved this series. The idea of empty quads was great. I started and restarted this puzzle dozens of times. Thought I had proven it was broken so I even tried to ask for a hint, and then I saw my logical error and it all fell into place. My hint is simply trust the things you’re sure of, but be sure you’re right!
on 27. October 2023, 17:29 by pms_headache
OMG this one has vexed me since it was published. I loved this series. The idea of empty quads was great. I started and restarted this puzzle dozens of times. Thought I had proven it was broken so I even tried to ask for a hint, and then I saw my logical error and it all fell into place. My hint is simply trust the things you’re sure of, but be sure you’re right!
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Thank you for putting the time into not only solving it but also giving it second chances when it was being recalcitrant! We're delighted you pushed through and enjoyed it in the end :D
on 22. October 2023, 20:17 by Fool on Hill
This was a tightly constructed toughie which took some working out. Some very nice interactions between the clues, and variety in the way the Schrödinger cells resolved and what they contributed.
on 22. October 2023, 17:56 by JayForty
Great puzzle! Took some thinking but all very fair and rewarding. Amazingly clever construction! Thanks :)
on 20. October 2023, 04:17 by ViKingPrime
For the briefest of moments, I thought I had broken the puzzle and was ready to scrap the entire thing, but I had to double-check, just to make sure... let this guide you, future solver. If you think you may have broken the puzzle, it may be true but ask yourself "is there any way this is possible?" It may save you a lot of time and heartache.
Well done to both of you! This was an incredible puzzle pack.
on 18. October 2023, 20:32 by Jds2
FYI. the answer check in the CtC app appears not to be working perfectly. It only works if you erase all the 0s.
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Thank you, yes that's right. I'll update the page to explain that.
on 18. October 2023, 20:32 by giladooshlon
It's amazing what can be accomplished with those counting circles. Wonderful construction and very very hard.
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Thank you! Yes it's such a cool ruleset with so much potential! It was very cool to work with its founding father on this series!
