Colossal Masyu Masyu-Sudoku
(Published on 8. October 2023, 21:52 by Christounet)
I have contemplated the idea of making a loop puzzle for a long time. One of my most memorable experience of solving a loop puzzle was the marvelous Masyu/Sudoku hybrid by Jesper. There was something about Masyu that I found really enjoyable, so it naturally evolved into the idea of setting a giant one ! In this colossal puzzle, you will not only have to draw a Masyu loop in the big grid, but in the sudoku grid as well :) Enjoy !
The puzzle :
Before I introduce you to the rules, 2 quick words about the puzzle. Firstly, like in my other colossal puzzle, after the first few steps, the path will not be strictly linear, but rather diverge in some parallel paths that will converge eventually. Secondly, you will notice a weird rule about the R9C9 cell of the sudoku. The reason I needed to add that little trick is because my indexing ruleset would not have allowed a valid grid otherwise. With my indexing, the loop would need to take 9×45 = 405 cells in the big grid, but an orthogonally connected loop will always have an even number of cells, so I had to make up that "off-by-one" rule to "correct" this annoying mathematical reality and keep my initial ruleset. This rule will apply very locally, without interfering with the overall logic, so I think and hope it shouldn't be too annoying.
Rules :
Sudoku grid :
- Standard 9x9 sudoku, where the digit in each cell of the Sudoku grid must equal the number of cells visited by the loop in the corresponding 3x3 box in the Masyu grid.
- For R9C9 (dashed circle), the count is off by one, i.e. the corresponding 3x3 box in Masyu will have one more or one less loop cell than the digit in R9C9. (Example : if R9C9 = 6, it indicates 5 or 7 loop cells)
- In the sudoku grid, draw a Masyu loop (See below for detailed rules of a Masyu loop). Not all cells are necessarily visited by the loop. In this grid, all the 1's and 2's are considered respectively as white and black Masyu pearls (as in Jesper's Masyu puzzle).
- Squares : a digit in a square gives the number of cells visited by the loop in the up to 9 surrounding cells (including itself). ALL valid squares are given.
Masyu grid :
- Draw a non branching non crossing closed loop through the center of orthogonally connected cells, that must visit all given pearls in the grid.
- Black pearl : the loop must turn on the pearl, and go straight through both adjacent cells along the loop.
- White pearl : the loop must go straight through the pearl, but turn in at least one adjacent cell along the loop.
- Grey pearl : it must behave as a white or a black pearl, to be determined by the solver.
- ALL possible black pearls of the Masyu grid are given (i.e. if the loop makes a turn and go straight through both adjacent cells along the loop, there should be a given black or grey pearl on the turn)
Diagram example of the rules (negative constraints in red) :
Solution code: For the central 9x9 region of the 27x27 Masyu grid, the number of turns of the loop in each of the 9 rows, from top to bottom (9 digits in total).
Comments
on 30. June 2024, 02:58 by MaizeGator
Beautiful construction! I loved the ambiguous Masyu clues and the interplay between the grids. I would love to set one of these someday.
on 18. April 2024, 08:19 by Tacosian
Fantastic puzzle. I really loved this one.
on 13. March 2024, 00:24 by Piatato
Awesome! Very smooth, and quite meditative! The ruleset felt very intuitive and easy to get used to. :)
on 28. October 2023, 05:08 by dumediat
My first colossal puzzle! It was great fun slowly making progress around the grids, thank you very much!
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@dumediat : Nice ! I am glad you enjoyed the experience. I can only encourage you to try the other ones if you enjoy getting lost in those big grids. I believe there are 6 colossal puzzles out there to this day. They are so much fun to set and solve !
on 15. October 2023, 05:29 by wooferzfg
Really fun, thanks!
on 14. October 2023, 20:37 by ddx01
Took me forever, but it was lots of fun! Thank you, Christounet! ^_^
on 14. October 2023, 08:24 by henrypijames
In the sudoku grid, 1s and 2s act like pearls - but does it mean they all have to be visited by the loop? Because you're very specific that the two parts of the rules are separate, and in the sudoku grid part, there's no explicit requirement that all pearls (1s and 2s) must be visited.
Basically, the sentence in the first part of the rules, "See below for detailed rules of a Masyu loop", is very problematic, because it doesn't say which subparts of the second part constitute "detailed rules of a masyu loop", and which other subparts are extra rules that don't apply to the first part. One might think that all of the second part are masyu rules and therefore binding for the sudoku grid. This is why other people have been confused about the relationship between those two parts as well.
A better way to organize the rules would be to make it three parts: 1. General masyu rules applicable to both grids, 2. Rules for the colossal grid, 3. Rules for the sudoku grid (this part last because it refers to the other two parts). Generally, forward reference (to something that is yet to come) should be avoided if at all possible, because it's counter to the way people think and learn things.
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@henrypijames : Thanks for your input on the rules presentation. It was indeed not easy to formulate them without making too many repeats in an already long ruleset. I will try to rewrite them this weekend.
So, to answer your specific question : yes, all the 1s and 2s in the sudoku grid have to be visited by the loop and behave as white/black pearls. (See Jesper's puzzle for an example). Sorry for omitting this important detail !
on 13. October 2023, 07:10 by Agent
Great puzzle, a fun marathon!
on 9. October 2023, 23:57 by Niverio
Long and fun, as is the usual case for all the colossal puzzles!
on 9. October 2023, 13:33 by Christounet
Clarification in the rules.
on 9. October 2023, 13:23 by ridesdragons
so something that confused me and a friend in the rules and example regarding the negative constraints. I was under the impression that the black pearls on the sudoku board were also restricted, in that if you had a bend followed by 2 straights, it must be a 2, and in the example, I see a bend followed by 2 straights indeed being marked as wrong. I can see it's also an 8 without being a square as well, but I just thought it was triggering both negative constraints. in the puzzle, though, we ran into an issue when assuming the black pearl constraint was on the sudoku board as well.
would you mind clarifying whether the black pearl constraint applies to the sudoku board as well or not?
@ridesdragons : Hello ! Thanks for trying the puzzle. As you can see, the rules are written in 2 distinct parts, one for the Sudoku grid, one for the Masyu grid. The black pearl negative constraint is only written for the Masyu grid. I will make a little update to clarify this in case anyone else gets confused. Have fun solving !
on 9. October 2023, 09:46 by Jesper
Awesome puzzle, was a lot of fun, thanks!
on 9. October 2023, 05:17 by Koalagator2
Amazing! I would personally rank it a 5-star difficulty due to it's length, although no step is individually hard.
on 8. October 2023, 22:37 by lerroyy
Very nice!
