Renban-na-na-na-na-na
(Published on 18. March 2022, 02:30 by SirSchmoopy)
Links to play:
CTC
F-Puzzles
Walkthrough
Standard Rules:
Normal sudoku rules apply.
Normal renban rules apply. Digits along a pink line form a set of consecutive digits in any order without repeats.
Cycle Definitions:
Let a cycle be the chain of cells along a single row created by going to the column indexed by the digit of first cell, then the column indexed by that cell, etc. until returning to the first cell.
Let the order of a cycle be the number of unique digits contained in a cycle.
For a concrete example, 5 in R1C1 -> 2 in R1C5 -> 1 in R1C2 would form an order 3 cycle.
Renban Cycle Rules:
Along with normal Renban rules, the orders of cycles along renban lines create a set of consecutive digits in any order without repeats.
n.b. - For a given renban line, the set of the orders of the cycles is not necessarily the same set created by the digits themselves. For instance, it would be perfectly valid for a 3-cell renban line to have digits of 8,7, and 9, and cycle orders of 3,2, and 1.
See the solved 6x6 for an example of a valid puzzle with this ruleset. Cycles are shaded for clarity.
(If you're curious, the name of this puzzle was taken from Simon's description of order 2 cycles as cells that point to each other going 'na-na-na-na-na' from one of my other puzzles that was featured on Cracking The Cryptic )
Solution code: Row 3 + Row 9 (18 digits, no spaces)
Comments
on 10. September 2022, 05:35 by starwarigami
Fantastic construction!
on 19. July 2022, 21:28 by Droi
Mindf*ck of a puzzle, in a good way. Great as usual, and I appreciate the walkthrough, had to refer to it twice and once to fix a mistake of mine.. Otherwise I would have abandoned this very nice puzzle!
on 26. April 2022, 04:25 by SimplePurpleFrog
Wow! What a stunning puzzle. Very hard, had to restart several times, but eventually cracked it.
The logic is mind bending but solid & clean. The break in is, interestingly, not the hardest part!
on 3. April 2022, 19:40 by SirSchmoopy
Adding link to a walk through now that the puzzle has been available for a while.
on 30. March 2022, 18:38 by tlepetit
Loved the first one, and this one delivers!
Very nice ruleset with some new mind-binding deduction. I hope to see some more of those.
on 24. March 2022, 07:34 by Playmaker6174
I feel quite bad at myself for choosing this one as my very first cycle puzzle xD
Lots of intricate and difficult steps to think ahead but I really enjoyed how everything connects together and in an interesting way too :}
on 19. March 2022, 08:06 by henrypijames
As I said after test-solving it: This is a significantly more elegant puzzle than the one Simon has solved - I hope it gets featured too, if only just to watch Simon struggle to find a way to pencilmark the cycle lengths :D (which I did with coloring in the rainbow order).
on 19. March 2022, 04:56 by twobear
Fascinating puzzle with very interesting logic. Thank you!
on 18. March 2022, 19:06 by Myxo
In the example, doesn't the renban line in the middle have 2 cycles of length 2?
[SirSchmmopy] - I don't believe so. the 5 is order 2 (5 -> 3 ), the 6 is order 3 (6 -> 1 -> 4), and the 4 is order 1. Where exactly are the 2 order-2 cycles you're seeing?
[Myxo] - You are right, I got confused by the coloring, but 4 and 5 actually do not reference each other in row 4. Sorry.
on 18. March 2022, 11:57 by MagnusJosefsson
Great puzzle! Remarkable achievement to make this complex ruleset work so well using only the renban/cycle lines. Quite a difficult puzzle, but very rewarding!
on 18. March 2022, 06:20 by Arashdeep Singh
Very very hard but also very very beautiful.
