Fog-stomefel Ring
(Published on 15. May 2024, 17:00 by Flinty)
Normal Sudoku rules apply.
Place the digits 1-9 so that they do not repeat in any row, column, or 3x3 box.
Fog of War
Most of the grid is covered in fog. Placing correct digits reveals the fog, no guessing is required.
Killer Cages
Digits in cages must sum to the number in the top-left corner, and digits cannot repeat within a cage.
German Whispers
Two cells connected by a green line must have a difference of at least 5.
Special Thanks
Here is a link to a Numberphile YouTube video, with a guest appearance by Simon Anthony from CtC, explaining the 'set theory' logic that is used in this puzzle. Named after the setter Phistomefel who first proved it.
Hints available below - may only work on Desktop
To play this puzzle please click here: Play CTC
Hint - What you may have missed
The cage in box 9 has a sneaky cell in the fog.
Hint - Where to start
This puzzle relies on an understanding of the Phistomefel Ring set theory. The digits in the four corners are exactly the same as the digits in the two eight-cell 44 cages.
Hint - I'm still stuck at the start
The 44 cages must contain two full sets of the digits 2-9 (There isn't a 1), therefore there isn't a 1 in the corners. The 16 cage is impossible without a 1, so where can we place that? We can do maths on the remaining corner values to work out R2C2. 44+44=88. 16+17+26+21=80, but we need to remove 1 because the 16 cage only contributes 15 in value in the corner. 88-79=9. R2C2 is 9.
Hint - It's quite tricky this puzzle
If you are still in the corners, you have likely pencilmarked the Box 1 and Box 9 cages, using up the quantity of 6s (from the two sets), but haven't yet used a 5. You still need to find a home for a second 9. The 44 cages are important because they are almost extra regions and force a lot of logic around corners.
Solution code: Digits in Row 5
Comments
on 25. July 2024, 06:11 by ostio456
I learned of the Phistomefel ring some time back from the CtC channel but had never got a chance to give it a go in practice... until today. This quickly pushed its way to one of my favourite puzzles of all time. Loved the logic from start to finish!
on 24. July 2024, 03:59 by ostio456
I learned of the Phistomefel ring some time back from the CtC channel but had never got a chance to give it a go in practice... until today. This quickly pushed its way to one of my favourite puzzles of all time. Loved the logic from start to finish!
on 20. July 2024, 15:50 by glum_hippo
Took me far too long due to a graphic subtlety that I could not see for the first several minutes. RIP my eyes
on 20. July 2024, 14:14 by geronimo92
Hints here are always welcome and useful... If you dont need them, don't ask the setter to remove them please ! Everyone is free to watch them or not thanks a lot
on 10. June 2024, 13:44 by ave
I didn't find it "EASY", as per ** suggests.
But I'm glad I persisted! It was a struggle, but completing a puzzle is always a joy.
on 26. May 2024, 17:31 by CSStead
Really enjoyable!
on 24. May 2024, 23:46 by Playmaker6174
The follow-up part after the break-in was actually pretty nice, thanks for the fun :)
on 20. May 2024, 19:27 by Meech
Really loved that puzzle really well done
on 19. May 2024, 11:41 by meatbox
I normally struggle with the two star puzzles, but got the first digit on my own. I did need the hints, and managed to complete without ever being completely blocked. Thanks for a fun puzzle.
on 18. May 2024, 11:06 by walaura
This was so much fun!! Thank you, loved the box 5 surprise
on 16. May 2024, 19:41 by s1mn
Really enjoyed this! Lots of fun to solve, and felt hard enough that I felt very clever for solving it. :D
on 16. May 2024, 18:10 by Zarlino
Loved this puzzle - the first Phistomefel ring I've been able to do. Thank you very much for setting it.
on 16. May 2024, 15:44 by Fra314
Brilliant puzzle, especially the break-in. Clever and super fun!
on 16. May 2024, 13:13 by SirWoezel
Nice flow. Thanks for the puzzle.
on 16. May 2024, 11:40 by horseradish1
I'll be honest. I'm only barely capable of solving most 2 star puzzles on here, and I felt like I breezed through the logic of this one compared to what I try. It was absolutely beautiful to solve, but I feel like the difficulty comes from whether you understand the Phistomefel ring or not, and I've watched enough Cracking the Cryptic that it's second nature to me. Well done!
on 16. May 2024, 09:57 by Sumanta(ANU)
Very nice and beautiful puzzle...Thanks
on 16. May 2024, 08:20 by Flinty
Thank you for the kind comments. :)
on 16. May 2024, 06:52 by DarrenBurnett
This is a fantastic puzzle. I loved it.
on 16. May 2024, 00:01 by sujoyku
Thank you for the amazing puzzle, Flinty! This time I did not need the hints but I think it is very nice of you to include them. It is like a safety net giving the option to look for help if one might feel the need. Thank you for setting and sharing this gem!
on 15. May 2024, 22:35 by briansometimes
Thoroughly enjoyed this.
on 15. May 2024, 21:47 by sacklunch
Beautiful puzzle, what gorgeous interaction between the cages in the opening. Absolutely loved it. Not too difficult, especially with the killer calculator turned on in CTC :)
on 15. May 2024, 20:26 by emsou
@Piatato I didn't use the hints myself, but I think they'd be handy if I wanted to send this puzzle to a few friends of mine. This board (and the included hints) is a good start for someone who's never used the Phistomefel ring or the pigeonhole principle to solve a sudoku before.
on 15. May 2024, 20:22 by Piatato
The puzzle solves very smoothly, and the telegraphing is excellent. We maybe don't need so many hints?
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Flinty: If the hints help make the puzzle more accessible for even one person, then it's worth the effort. :)
on 15. May 2024, 20:21 by stonetim
Very fun puzzle. Thank you for setting!
on 15. May 2024, 18:51 by hardline35
Love how the puzzle converges to center! Thanks
on 15. May 2024, 18:51 by ludvigr04
Very nice Puzzle!
on 15. May 2024, 18:10 by goodcity
Great puzzle with some unexpected logic !
on 15. May 2024, 18:08 by wuc
Great puzzle. Smooth and clever. Thx.
