Implications of Parity
(Published on 30. July 2022, 13:06 by Niverio)
Another note: I am not exactly certain how hard this puzzle is, mainly cause of how unique some of the deductions are. I am going to release it as a 5-star to be safe, although depending on solver capability and with the right approach to this puzzle, that might vary quite a bit. So if you solve and enjoy the puzzle, leave a comment to explain how your journey around the Implications of Parity commenced! I am looking forward to reading them.
Rules:
- Normal Sudoku rules apply.
- Cells containing a gray circle must contain odd digits.
- Cells containing a gray square must contain even digits.
In the outer ring (Rows 1 and 9 + Columns 1 and 9) there are 4 given lines. The lines are ambiguous, and are from the following:
- One is a German Whispers line.
- One is a Renban line.
- One is a Between line.
- One is a Thermometer.
In the inner ring (Rows 2 and 8 + Columns 2 and 8) there are 8 given dots. On this ring, the dots that belong to the same row/column have the same constraint property:
- One row/column's pair is a V dot pair.
- One row/column's pair is an X dot pair.
- One row/column's pair is a white dot pair.
- One row/column's pair is a black dot pair.
In Box 5 (Middle Box), all 4 dots have a different property:
- One is a V dot.
- One is an X dot.
- One is a white dot.
- One is a black dot.
You can play the puzzle online in F-Puzzles or in the CTC Software.
Enjoy!
Clarifications:
- Regarding Box 5, just assume that the 4 gray dots are replaced with the 4 different constraints in some order. It is possible that a dot is functioning as 2 constraint types at the same time. This has no impact on the other dots and you can pick which constraint type that dot uses.
Example: If a gray dot connects 2 and 3, you can decide whichever of V or white dot to use to make the rule for Box 5 work in compliance with Sudoku rules.
- In the outer ring, it is possible that a line satisfies more than one of the 4 specified constraints. What's important is that you can assign each line one of the 4 constraints, so that all 4 line types will be used by 4 different lines.
Solution code: Row 6 followed by Column 6 (No commas or spaces, 18 digits)
Comments
on 13. September 2024, 12:30 by Playmaker6174
Holy sweet cheese, that was wonderful! You really milked pretty much every single familiar constraint to the core in here x)
My favorite part was the one breakthrough around the lines and how the order of the parity cells in r28c28 impacted on everything in here :)
on 11. September 2023, 09:05 by Xendari
what the heck
on 8. August 2023, 14:29 by Bankey
Amazing puzzle! Had abandoned it half-way earlier, but got thru today. Thanks, @ Niverio :).
on 4. February 2023, 02:38 by Myxo
Amazing puzzle!
on 16. August 2022, 21:20 by Qodec
Milking every clue to the max, that's how I like it!
on 8. August 2022, 09:04 by filuta
very fun puzzle for me, I liked the unusual nature of some deductions.
on 7. August 2022, 01:52 by Agent
This is one of my favourite ambiguity puzzles so far. Thanks!
on 1. August 2022, 17:12 by henrypijames
Only 3½ for me - I was surprised how smoothly I can through.
Also: Isn't the circle for the central cell unnecessary? Doesn't it only have two options anyway, both odd?
on 1. August 2022, 01:29 by BHUNTER47
Loved this idea. It was fairly easy to spot that I could divide each of the lines into two groups fairly quickly, and the dot rows the same...but getting to the spot where I broke past that took a lot of thought!
on 31. July 2022, 19:59 by nunc
Thanks for this puzzle, very satisfying. This is my first 5*-rated puzzle (difficulty) that I managed to solve. Although it did seem to me to be a 4*, because I didn't find it terribly hard.
Congrats on solving your first 5-star puzzle! And yes, this puzzle is rather unique but not the most difficult. I hope you enjoyed, and thank you so much for the solve and comment :)
on 31. July 2022, 12:21 by Piatato
Amazing puzzle! A lot of fun and, yeah, not horribly hard. :-D
on 31. July 2022, 09:10 by cdwg2000
Very beautiful design logic, highlighting the main features of several rule sets, clever interaction, enjoy the whole logic. This is my logic problem solving process,
【202207311218-哔哩哔哩】 https://b23.tv/gxRHuBX
on 30. July 2022, 18:03 by KNT
This puzzle was very neat, however every deduction felt super natural to me (I was expecting much more brutal, not that that's a bad thing). I can now understand why you said "solve times may vary".
on 30. July 2022, 17:34 by cdwg2000
Very nifty rule interaction. I want to take the time to make a logic problem solving process.
on 30. July 2022, 17:15 by Vebby
Awesome puzzle! Very intelligent construction. Felt like a high 4 stars to me. It requires a few key deductions after which it yields quite smoothly towards the end. Thanks Niverio! :)
on 30. July 2022, 13:34 by grkles
I loved this puzzle. There are some really funky deductions that were not easy to get my head around, but they were so rewarding when I did. They felt like epiphanies.
